<PAGE>   1
    As filed with the Securities and Exchange Commission on May 21, 1997
                                        Registration No. 333-
                                                             -------------------

--------------------------------------------------------------------------------

                     SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C.  20549

                            --------------------

                                  FORM S-8
                           REGISTRATION STATEMENT
                                    UNDER
                         THE SECURITIES ACT OF 1933

                            --------------------

                           CLIFFS DRILLING COMPANY
           (Exact Name of Registrant as specified in its charter)


          Delaware                                             76-0248934
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                             Identification No.)

                          1200 Smith Street, Suite 300
                             Houston, Texas  77002
                    (Address of principal executive offices)
                                        
                            --------------------
                                        
                           CLIFFS DRILLING COMPANY
                           1988 INCENTIVE EQUITY PLAN
                            (Full Title of the Plan)

                            --------------------

                               EDWARD A. GUTHRIE
                           Vice President -- Finance
                            Cliffs Drilling Company
                          1200 Smith Street, Suite 300
                             Houston, Texas  77002
                                 (713) 651-9426
           (Name, address and telephone number of agent for service)

                                    Copy to:
                             W. GARNEY GRIGGS, Esq.
                            Griggs & Harrison, P.C.
                           1301 McKinney, Suite 3200
                             Houston, Texas  77010
                                 (713) 651-0600 


                            --------------------

                        CALCULATION OF REGISTRATION FEE


<TABLE>
<CAPTION>
============================================================================================================
                                                   Proposed              Proposed
       Title of                                     Maximum               Maximum
      Securities             Amount to          Offering Price           Aggregate             Amount of
   to be Registered        be Registered         Per Share (1)      Offering Price (1)      Registration Fee
------------------------------------------------------------------------------------------------------------
  <S>                     <C>                       <C>                 <C>                    <C>
     Common Stock,
  par value $0.01         160,000 shares            $65.0625             $10,410,000             $3,154.55
      per share
============================================================================================================
</TABLE>

(1)  Estimated solely for the purpose of calculating the registration fee in
     accordance with Rule 457(c) and 457(h), based on the average of the high
     and low prices of the Company's Common Stock on May 16, 1997, as reported
     on the New York Stock Exchange.
<PAGE>   2
                                    PART II

              INFORMATION REQUIRED IN THE REGISTRATION STATEMENT



ITEM 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE

         Cliffs Drilling Company (the "Company") incorporates herein by
reference the following documents filed with the Securities and Exchange
Commission (File No. 0-16703):

         (1)     The Annual Report of the Company on Form 10-K for the fiscal
year ended December 31, 1996;

         (2)     The Quarterly Report of the Company on Form 10-Q for the
quarter ended March 31, 1997;

         (3)     The Proxy Statement of the Company dated April 25, 1997; and

         (4)     The description of the common stock, par value $0.01 per share
(the "Common Stock"), of the Company contained in the Company's Registration
Statement on Form 8-A, filed March 11, 1997.

         All documents filed by the Company pursuant to Sections 13(a), 13(c),
14 and 15(d) of the Securities Exchange Act of 1934, as amended  (the "Exchange
Act") after the date of this Registration Statement and prior to the filing of
a post-effective amendment which indicates that all securities offered hereby
have been sold or which deregisters all such securities then remaining unsold,
shall be deemed to be incorporated by reference in this Registration Statement
and to be a part hereof from the date of filing such documents.

         Any statement contained herein or in any document incorporated or
deemed to be incorporated by reference herein shall be deemed to be modified
and superseded for purposes of this Registration Statement to the extent such
statement is modified or superseded by a statement contained in any other
subsequently filed incorporated document or in any accompanying prospectus
supplement.

ITEM 4.  DESCRIPTION OF SECURITIES

         Not applicable.

ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL

         Not applicable.

ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS

         General

         Article Ninth of the Company's Certificate of Incorporation ("Article
Ninth") requires the Company to indemnify its directors, officers and certain
other individuals to the full extent permitted by the Delaware General
Corporation Law ("Delaware GCL") or other applicable laws and allows the
Company to enter into agreements with any person to provide greater or
different indemnification than that provided in Article Ninth or the Delaware
GCL.

         Article Tenth of the Company's Certificate of Incorporation ("Article
Tenth") limits the personal liability of the Company's directors to the Company
or its shareholders to the full extent permitted by the Delaware GCL, which
currently permits directors to be protected from monetary damages for breach of
their fiduciary duty of care.  This limitation has no effect on claims arising
under the federal securities laws.





                                       2
<PAGE>   3
         Indemnification and Insurance

         Under the Delaware GCL, directors and officers as well as other
employees and individuals may be indemnified against expenses (including
attorneys' fees), judgments, fines and amounts paid in settlement in connection
with specified actions, suits or proceedings, whether civil, criminal,
administrative or investigative (other than an action by or in the right of the
corporation such as a derivative action) if they acted in good faith and in a
manner they reasonably believed to be in or not opposed to the best interests
of the corporation and, with respect to any criminal action or proceeding, had
no reasonable cause to believe their conduct was unlawful.  A similar standard
of care is applicable in the case of actions by or in the right of the
corporation, except that indemnification extends only to expenses (including
attorneys' fees) incurred in connection with defense or settlement of such an
action, and the Delaware GCL requires court approval before there can be any
indemnification where the person seeking indemnification has been found liable
to the corporation.

         Article Ninth provides that each person who is or was or had agreed to
become a director or officer of the Company, and each such person who is or was
serving or who had agreed to serve at the request of the Board of Directors or
an officer of the Company as an employee or agent of the Company, or as a
director, officer, employee or agent of another corporation, partnership, joint
venture, trust or other enterprise (including the heirs, executors,
administrators or estate of such person) shall be indemnified by the Company to
the full extent permitted by the Delaware GCL or any other applicable laws as
presently or hereafter in effect.  Under Article Ninth, subject to the
limitations on indemnification imposed by the Delaware GCL, a large award
against an officer or director or other appropriate individual could be paid by
the Company, which could materially reduce the assets of the Company.

         Article Ninth provides that, without limiting the generality or effect
of the foregoing, the Company may enter into one or more agreements with any
person which provide for indemnification greater or different than that
provided in Article Ninth.  Finally, Article Ninth and Article Tenth each
provide that any repeal or modification of such article shall not adversely
affect any right or protection existing thereunder immediately prior to such
repeal or modification.

         The Company has entered into agreements with each of its directors and
certain officers providing for indemnification broader than that provided by
Article Ninth.  Each of the directors and certain officers are entitled to
indemnification pursuant to the indemnification agreements whether his or her
acts, failure to act, neglect or breach of duty giving rise to the right to
indemnity thereunder occurred prior or subsequent to the date of such
agreement.  Such right, however, would not be available with respect to any
act, failure to act, neglect or breach of duty of a director or officer
occurring prior to the date such person became a director or officer of the
Company.

         One of the purposes of entering into such indemnification agreements
was to specify the extent to which the directors and certain officers may
receive indemnification under circumstances in which indemnity would not
otherwise be provided by Article Ninth.  Such agreements entitle the directors
and officers to indemnification as expressly provided by Article Ninth and to
indemnification for any amount which a director or officer is or becomes
legally obligated to pay relating to or arising out of any claim made against
such director or officer because of any act, failure to act or neglect or
breach of duty, including, without limitation, any actual or alleged error,
misstatement or misleading statement, which such director or officer commits,
suffers, permits or acquiesces in while acting in the director's or officer's
position with the Company.  The right to receive payments under the
indemnification agreements in excess of those expressly provided in Article
Ninth would not be permitted, however, in connection with any claim against a
director or officer:

                 (i)      which results in a final, nonappealable order against
         the director or officer to pay a fine or similar governmental
         imposition which the Company is prohibited by applicable law from
         paying; or

                 (ii)     to the extent based upon or attributable to the
         director or officer gaining in fact a personal profit to which he or
         she was not legally entitled, including, without limitation, profits
         made from the purchase and sale of equity securities of the Company
         which are recoverable by the Company pursuant to Section 16(b) of the
         Exchange Act and profits arising from transactions in publicly traded
         securities of the Company which were effected by the director or
         officer in violation of Section 10(b) of the Exchange Act, including
         Rule 10b-5 promulgated thereunder.





                                       3
<PAGE>   4
         Another purpose of the indemnification agreements is to provide the
directors or officers with increased assurance of indemnification by
prohibiting the Company from adopting any amendment to the Company's
Certificate of Incorporation or Bylaws which would have the effect of denying,
diminishing or encumbering their rights to indemnification pursuant thereto or
to the Delaware GCL or any other law as applied to any act or failure to act
occurring in whole or in part prior to the effective date of such amendment.

         At present there is no pending litigation or proceeding involving a
director or officer of the Company in which indemnification would be required
or permitted by the indemnification agreements.  The Board of Directors is not
aware of any threatened litigation or proceeding which may result in a claim
for indemnification under any such indemnification agreement.

         Elimination of Liability in Certain Circumstances

         Under the Delaware GCL, Article Tenth protects the Company's directors
against monetary damages for breaches of their duty of care, except as set
forth below.  The inclusion of Article Tenth in the Company's Certificate of
Incorporation means that the Company and its shareholders forego the ability to
bring a cause of action against a director for monetary damages for certain
breaches of fiduciary duty, including actions in connection with proposals for
the acquisition of control of the Company.  Directors remain liable for
breaches of their duty of loyalty to the Company and its shareholders, as well
as acts or omissions not in good faith or which involve intentional misconduct
or a knowing violation of law and transactions from which a director derives
improper personal benefit.  Also, Article Tenth does not eliminate director
liability under Section 174 of the Delaware GCL, which makes directors
personally liable for unlawful dividends or unlawful stock repurchases or
redemptions and expressly sets forth a negligence standard with respect to such
liability.

         Although Article Tenth provides directors with protection from awards
of monetary damages for breaches of the duty of care, it does not eliminate the
directors' duty of care.  Accordingly, Article Tenth has no effect on the
availability of equitable remedies such as an injunction or rescission based
upon a director's breach of the duty of care.  The provisions of Article Tenth
which eliminate liability as described above applies to officers of the Company
only if they are directors of the Company and are acting in their capacity as
directors, and does not apply to officers of the Company who are not directors.

ITEM 7.  EXEMPTION FROM REGISTRATION CLAIMED

         Not applicable.

ITEM 8.  EXHIBITS

         The following instruments and documents are included as Exhibits to
this Registration Statement.   Exhibits incorporated by reference are so
indicated by parenthetical information.

<TABLE>
<CAPTION>
EXHIBIT
NUMBER   EXHIBIT
------   -------
   <S>           <C>

   4.1  -        Certificate of Incorporation of the Company, as amended (Incorporated by reference to Exhibit 3.1 to
                 the Company's Registration Statement on Form S-1, No. 33-23508)

   4.2   -       Bylaws of the Company (Incorporated by reference to Exhibit 3.2 to the Company's Registration Statement
                 on Form S-1, No. 33-23508)

   4.3   -       Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to Exhibit 10.8 to the
                 Company's Registration Statement on Form S-1, No. 33-23508)

   4.3.1 -       Amendment No. 1 to the Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to
                 Exhibit 10.7.1 to the Company's Form 10-K for the fiscal year ended December 31, 1993)
</TABLE>





                                       4
<PAGE>   5
<TABLE>
 <S>             <C>
   4.3.2 -       Amendment No. 2 to the Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to
                 Exhibit 10.7.2 to the Company's Form 10-K for the fiscal year ended December 31, 1993)

   4.3.3 -       Amendment No. 3 to the Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to
                 Exhibit 10.7.3 to the Company's Form 10-K for the fiscal year ended December 31, 1996)

  *5.1   -       Opinion of Griggs & Harrison, P.C.

 *23.1   -       Consent of Ernst & Young LLP

  23.2   -       Consent of Griggs & Harrison, P.C. (included in Exhibit 5.1)

 *23.3   -       Consent of Huddleston & Co., Inc.

</TABLE>

---------------                                   

*Filed herewith


ITEM 9.  UNDERTAKINGS


   (a)   The Company hereby undertakes:

    (1)   To file, during any period in which offers or sales are being made, a
post-effective amendment to this Registration Statement:

        (i) To include any prospectus required by section 10(a)(3) of the
   Securities Act of 1933, as amended (the "Securities Act");

       (ii) To reflect in the prospectus any facts or events arising after the
   effective date of the Registration Statement (or the most recent
   post-effective amendment thereof) which, individually or in the aggregate,
   represent a fundamental change in the information set forth in the
   Registration Statement.  Notwithstanding the foregoing, any increase or
   decrease in volume of securities offered (if the total dollar value of
   securities would not exceed that which was registered) and any deviation
   from the low or high end of the estimated maximum offering range may be
   reflected in the form of prospectus filed with the Commission pursuant to
   Rule 424(b) if, in the aggregate, the changes in volume and price represent
   no more than a 20% change in the maximum aggregate offering price set forth
   in the "Calculation of Registration Fee" table in the effective Registration
   Statement.

      (iii) To include any material information with respect to the plan of
   distribution not previously disclosed in the Registration Statement or any
   material change to such information in the Registration Statement;

provided, however, that paragraphs (i) and (ii) above do not apply if the
information required to be included in a post- effective amendment by those
paragraphs is contained in periodic reports filed by the Company pursuant to
Section 13 or Section 15(d) of the Exchange Act that are incorporated by
reference in this Registration Statement.

   (2)   That, for the purpose of determining any liability under the
Securities Act, each such post-effective amendment shall be deemed to be a new
registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.

   (3)   To remove from registration by means of a post-effective amendment any
of the securities being registered which remain unsold at the termination of the
offering.
   




                                       5
<PAGE>   6
   (b)   The Company hereby undertakes that, for purposes of determining any
liability under the Securities Act, each filing of the Company's annual report
pursuant to Section 13(a) or Section 15(d) of the Exchange Act (and, where
applicable, each filing of an employee benefit plan's annual report pursuant to
section 15(d) of the Exchange Act) that is incorporated by reference in the
Registration Statement shall be deemed to be a new registration  statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.

   (h)   Insofar as indemnification for liabilities arising under the
Securities Act may be permitted to directors, officers and controlling persons
of the Company pursuant to the provisions described under Item 6 above, or
otherwise, the Company has been advised that, in the opinion of the Securities
and Exchange Commission, such indemnification is against public policy as
expressed in the Securities Act and is, therefore, unenforceable.  In the event
that a claim for indemnification against such liabilities (other than the
payment by the Company of expenses incurred or paid by a director, officer or
controlling person of the Company in the successful defense of any action, suit
or proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the Company will, unless, in
the opinion of its counsel, the matter has been settled by controlling
precedent, submit to a court of appropriate jurisdiction the question whether
such indemnification by it is against public policy as expressed in the
Securities Act and will be governed by the final adjudication of such issue.





                                       6
<PAGE>   7
                                   SIGNATURES

   Pursuant to the requirements of the Securities Act of 1933, Cliffs Drilling
Company certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-8 and has duly caused this
Registration Statement or Amendment to be signed on its behalf by the
undersigned, thereunto duly authorized, in the City of Houston, State of Texas,
on May 21, 1997.


                                 CLIFFS DRILLING COMPANY
                                 
                                 
                                 By: /s/ Douglas E. Swanson                    
                                     ------------------------------------------
                                               Douglas E. Swanson
                                        Chairman of the Board, President 
                                    (Principal Executive Officer), and Director


         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement or Amendment has been signed by the following persons in
the capacities and on the dates indicated.

<TABLE>
<CAPTION>
             SIGNATURE                                    TITLE                         DATE
             ---------                                    -----                         ----
 <S>                                        <C>                                      <C>  

 /s/ Douglas E. Swanson                     Chairman of the Board, President         May  21, 1997
 ---------------------------------          (Principal Executive Officer),                        
     (Douglas E. Swanson)                   and Director                  
                                                                          
 /s/ M. M. Cone                             Director                                 May  21, 1997
 ---------------------------------                                                                
     (M.M. Cone)


 /s/ H. Robert Hirsch                       Director                                 May  21, 1997
 ---------------------------------                                                                
     (H. Robert Hirsch)


 /s/ Donald W. Keller                       Director                                 May  21, 1997
 ---------------------------------                                                                
     (Donald W. Keller)

 /s/ Robert M. McInnes                      Director                                 May  21, 1997
 ---------------------------------                                                                
     (Robert M. McInnes)


 /s/ Joseph E. Reid                         Director                                 May  21, 1997
 ---------------------------------                                                                
     (Joseph E. Reid)

 /s/ John D. Weil                           Director                                 May  21, 1997
 ---------------------------------                                                                
     (John D. Weil)


 /s/ Edward A. Guthrie                      Vice President - Finance                 May  21, 1997
 --------------------------------           (Principal Financial Officer)                                                      
     (Edward A. Guthrie)

 /s/ Cindy B. Taylor                        Vice President - Controller              May  21, 1997
 ---------------------------------          (Principal Accounting Officer)                        
     (Cindy B. Taylor)                                                                            
                                                                                                  
</TABLE>





                                       7
<PAGE>   8
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT                                                                                                      SEQUENTIALLY
NUMBER                                                                                                      NUMBERED PAGE
------                                                                                                      -------------
<S>              <C>
   4.1   -       Certificate of Incorporation of the Company, as amended (Incorporated by
                 reference to Exhibit 3.1 to the Company's Registration Statement on Form
                 S-1, No. 33-23508)

   4.2   -       Bylaws of the Company (Incorporated by reference to Exhibit 3.2 to the
                 Company's Registration Statement on Form S-1, No. 33-23508)

   4.3   -       Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference
                 to Exhibit 10.8 to the Company's Registration Statement on Form S-1,
                 No. 33-23508)

   4.3.1 -       Amendment No. 1 to the Cliffs Drilling Company 1988 Incentive Equity Plan
                 (incorporated by reference to Exhibit 10.7.1 to the Company's Form 10-K for the fiscal year
                 ended December 31, 1993)

   4.3.2 -       Amendment No. 2 to the Cliffs Drilling Company 1988 Incentive Equity
                 Plan (incorporated by reference to Exhibit 10.7.2 to the Company's Form 10-K for the fiscal
                 year ended December 31, 1993)

   4.3.3 -       Amendment No. 3 to the Cliffs Drilling Company 1988 Incentive Equity Plan
                 (incorporated by reference to Exhibit 10.7.3 to the Company's Form 10-K for the fiscal year
                 ended December 31, 1996)

  *5.1   -       Opinion of Griggs & Harrison, P.C.

 *23.1   -       Consent of Ernst & Young LLP

  23.2   -       Consent of Griggs & Harrison, P.C. (included in Exhibit 5.1)

 *23.3   -       Consent of Huddleston & Co., Inc.
---------------                                   
</TABLE>

*Filed herewith




                                      8
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{"company-data": {"conformed-name": "CLIFFS DRILLING CO", "cik": "0000831964", "assigned-sic": "1381", "irs-number": "760248934", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-27543", "film-number": "97612496"}, "business-address": {"street1": "300 CITICORP CENTER", "street2": "1200 SMITH ST", "city": "HOUSTON", "state": "TX", "zip": "77002", "phone": "7136519426"}, "mail-address": {"street1": "300 CITICORP CENTER", "street2": "1200 SMITH STREET", "city": "HOUSTON", "state": "TX", "zip": "77002"}, "former-company": {"former-conformed-name": "NEW CLIFFS DRILLING CO", "date-changed": "19880801"}}
1
    As filed with the Securities and Exchange Commission on May 21, 1997
                                        Registration No. 333-
                                                             -------------------

--------------------------------------------------------------------------------

                     SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C.  20549

                            --------------------

                                  FORM S-8
                           REGISTRATION STATEMENT
                                    UNDER
                         THE SECURITIES ACT OF 1933

                            --------------------

                           CLIFFS DRILLING COMPANY
           (Exact Name of Registrant as specified in its charter)

          Delaware                                             76-0248934
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                             Identification No.)

                          1200 Smith Street, Suite 300
                             Houston, Texas  77002
                    (Address of principal executive offices)
                                        
                            --------------------
                                        
                           CLIFFS DRILLING COMPANY
                           1988 INCENTIVE EQUITY PLAN
                            (Full Title of the Plan)

                            --------------------

                               EDWARD A. GUTHRIE
                           Vice President -- Finance
                            Cliffs Drilling Company
                          1200 Smith Street, Suite 300
                             Houston, Texas  77002
                                 (713) 651-9426
           (Name, address and telephone number of agent for service)

                                    Copy to:
                             W. GARNEY GRIGGS, Esq.
                            Griggs & Harrison, P.C.
                           1301 McKinney, Suite 3200
                             Houston, Texas  77010
                                 (713) 651-0600 

                            --------------------

                        CALCULATION OF REGISTRATION FEE
============================================================================================================
                                                   Proposed              Proposed
       Title of                                     Maximum               Maximum
      Securities             Amount to          Offering Price           Aggregate             Amount of
   to be Registered        be Registered         Per Share (1)      Offering Price (1)      Registration Fee
------------------------------------------------------------------------------------------------------------
Common Stock,
  par value $0.01         160,000 shares            $65.0625             $10,410,000             $3,154.55
      per share
============================================================================================================
(1)  Estimated solely for the purpose of calculating the registration fee in
     accordance with Rule 457(c) and 457(h), based on the average of the high
     and low prices of the Company's Common Stock on May 16, 1997, as reported
     on the New York Stock Exchange.
2
                                    PART II

              INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE

         Cliffs Drilling Company (the "Company") incorporates herein by
reference the following documents filed with the Securities and Exchange
Commission (File No. 0-16703):

         (1)     The Annual Report of the Company on Form 10-K for the fiscal
year ended December 31, 1996;

         (2)     The Quarterly Report of the Company on Form 10-Q for the
quarter ended March 31, 1997;

         (3)     The Proxy Statement of the Company dated April 25, 1997; and

         (4)     The description of the common stock, par value $0.01 per share
(the "Common Stock"), of the Company contained in the Company's Registration
Statement on Form 8-A, filed March 11, 1997.

         All documents filed by the Company pursuant to Sections 13(a), 13(c),
14 and 15(d) of the Securities Exchange Act of 1934, as amended  (the "Exchange
Act") after the date of this Registration Statement and prior to the filing of
a post-effective amendment which indicates that all securities offered hereby
have been sold or which deregisters all such securities then remaining unsold,
shall be deemed to be incorporated by reference in this Registration Statement
and to be a part hereof from the date of filing such documents.

         Any statement contained herein or in any document incorporated or
deemed to be incorporated by reference herein shall be deemed to be modified
and superseded for purposes of this Registration Statement to the extent such
statement is modified or superseded by a statement contained in any other
subsequently filed incorporated document or in any accompanying prospectus
supplement.

ITEM 4.  DESCRIPTION OF SECURITIES

         Not applicable.

ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL

         Not applicable.

ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS

         General

         Article Ninth of the Company's Certificate of Incorporation ("Article
Ninth") requires the Company to indemnify its directors, officers and certain
other individuals to the full extent permitted by the Delaware General
Corporation Law ("Delaware GCL") or other applicable laws and allows the
Company to enter into agreements with any person to provide greater or
different indemnification than that provided in Article Ninth or the Delaware
GCL.

         Article Tenth of the Company's Certificate of Incorporation ("Article
Tenth") limits the personal liability of the Company's directors to the Company
or its shareholders to the full extent permitted by the Delaware GCL, which
currently permits directors to be protected from monetary damages for breach of
their fiduciary duty of care.  This limitation has no effect on claims arising
under the federal securities laws.

                                       2
3
         Indemnification and Insurance

         Under the Delaware GCL, directors and officers as well as other
employees and individuals may be indemnified against expenses (including
attorneys' fees), judgments, fines and amounts paid in settlement in connection
with specified actions, suits or proceedings, whether civil, criminal,
administrative or investigative (other than an action by or in the right of the
corporation such as a derivative action) if they acted in good faith and in a
manner they reasonably believed to be in or not opposed to the best interests
of the corporation and, with respect to any criminal action or proceeding, had
no reasonable cause to believe their conduct was unlawful.  A similar standard
of care is applicable in the case of actions by or in the right of the
corporation, except that indemnification extends only to expenses (including
attorneys' fees) incurred in connection with defense or settlement of such an
action, and the Delaware GCL requires court approval before there can be any
indemnification where the person seeking indemnification has been found liable
to the corporation.

         Article Ninth provides that each person who is or was or had agreed to
become a director or officer of the Company, and each such person who is or was
serving or who had agreed to serve at the request of the Board of Directors or
an officer of the Company as an employee or agent of the Company, or as a
director, officer, employee or agent of another corporation, partnership, joint
venture, trust or other enterprise (including the heirs, executors,
administrators or estate of such person) shall be indemnified by the Company to
the full extent permitted by the Delaware GCL or any other applicable laws as
presently or hereafter in effect.  Under Article Ninth, subject to the
limitations on indemnification imposed by the Delaware GCL, a large award
against an officer or director or other appropriate individual could be paid by
the Company, which could materially reduce the assets of the Company.

         Article Ninth provides that, without limiting the generality or effect
of the foregoing, the Company may enter into one or more agreements with any
person which provide for indemnification greater or different than that
provided in Article Ninth.  Finally, Article Ninth and Article Tenth each
provide that any repeal or modification of such article shall not adversely
affect any right or protection existing thereunder immediately prior to such
repeal or modification.

         The Company has entered into agreements with each of its directors and
certain officers providing for indemnification broader than that provided by
Article Ninth.  Each of the directors and certain officers are entitled to
indemnification pursuant to the indemnification agreements whether his or her
acts, failure to act, neglect or breach of duty giving rise to the right to
indemnity thereunder occurred prior or subsequent to the date of such
agreement.  Such right, however, would not be available with respect to any
act, failure to act, neglect or breach of duty of a director or officer
occurring prior to the date such person became a director or officer of the
Company.

         One of the purposes of entering into such indemnification agreements
was to specify the extent to which the directors and certain officers may
receive indemnification under circumstances in which indemnity would not
otherwise be provided by Article Ninth.  Such agreements entitle the directors
and officers to indemnification as expressly provided by Article Ninth and to
indemnification for any amount which a director or officer is or becomes
legally obligated to pay relating to or arising out of any claim made against
such director or officer because of any act, failure to act or neglect or
breach of duty, including, without limitation, any actual or alleged error,
misstatement or misleading statement, which such director or officer commits,
suffers, permits or acquiesces in while acting in the director's or officer's
position with the Company.  The right to receive payments under the
indemnification agreements in excess of those expressly provided in Article
Ninth would not be permitted, however, in connection with any claim against a
director or officer:

                 (i)      which results in a final, nonappealable order against
         the director or officer to pay a fine or similar governmental
         imposition which the Company is prohibited by applicable law from
         paying; or

                 (ii)     to the extent based upon or attributable to the
         director or officer gaining in fact a personal profit to which he or
         she was not legally entitled, including, without limitation, profits
         made from the purchase and sale of equity securities of the Company
         which are recoverable by the Company pursuant to Section 16(b) of the
         Exchange Act and profits arising from transactions in publicly traded
         securities of the Company which were effected by the director or
         officer in violation of Section 10(b) of the Exchange Act, including
         Rule 10b-5 promulgated thereunder.

                                       3
4
         Another purpose of the indemnification agreements is to provide the
directors or officers with increased assurance of indemnification by
prohibiting the Company from adopting any amendment to the Company's
Certificate of Incorporation or Bylaws which would have the effect of denying,
diminishing or encumbering their rights to indemnification pursuant thereto or
to the Delaware GCL or any other law as applied to any act or failure to act
occurring in whole or in part prior to the effective date of such amendment.

         At present there is no pending litigation or proceeding involving a
director or officer of the Company in which indemnification would be required
or permitted by the indemnification agreements.  The Board of Directors is not
aware of any threatened litigation or proceeding which may result in a claim
for indemnification under any such indemnification agreement.

         Elimination of Liability in Certain Circumstances

         Under the Delaware GCL, Article Tenth protects the Company's directors
against monetary damages for breaches of their duty of care, except as set
forth below.  The inclusion of Article Tenth in the Company's Certificate of
Incorporation means that the Company and its shareholders forego the ability to
bring a cause of action against a director for monetary damages for certain
breaches of fiduciary duty, including actions in connection with proposals for
the acquisition of control of the Company.  Directors remain liable for
breaches of their duty of loyalty to the Company and its shareholders, as well
as acts or omissions not in good faith or which involve intentional misconduct
or a knowing violation of law and transactions from which a director derives
improper personal benefit.  Also, Article Tenth does not eliminate director
liability under Section 174 of the Delaware GCL, which makes directors
personally liable for unlawful dividends or unlawful stock repurchases or
redemptions and expressly sets forth a negligence standard with respect to such
liability.

         Although Article Tenth provides directors with protection from awards
of monetary damages for breaches of the duty of care, it does not eliminate the
directors' duty of care.  Accordingly, Article Tenth has no effect on the
availability of equitable remedies such as an injunction or rescission based
upon a director's breach of the duty of care.  The provisions of Article Tenth
which eliminate liability as described above applies to officers of the Company
only if they are directors of the Company and are acting in their capacity as
directors, and does not apply to officers of the Company who are not directors.

ITEM 7.  EXEMPTION FROM REGISTRATION CLAIMED

         Not applicable.

ITEM 8.  EXHIBITS

         The following instruments and documents are included as Exhibits to
this Registration Statement.   Exhibits incorporated by reference are so
indicated by parenthetical information.
EXHIBIT
NUMBER   EXHIBIT
------   -------
4.1  -        Certificate of Incorporation of the Company, as amended (Incorporated by reference to Exhibit 3.1 to
                 the Company's Registration Statement on Form S-1, No. 33-23508)

   4.2   -       Bylaws of the Company (Incorporated by reference to Exhibit 3.2 to the Company's Registration Statement
                 on Form S-1, No. 33-23508)

   4.3   -       Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to Exhibit 10.8 to the
                 Company's Registration Statement on Form S-1, No. 33-23508)

   4.3.1 -       Amendment No. 1 to the Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to
                 Exhibit 10.7.1 to the Company's Form 10-K for the fiscal year ended December 31, 1993)
4
5
4.3.2 -       Amendment No. 2 to the Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to
                 Exhibit 10.7.2 to the Company's Form 10-K for the fiscal year ended December 31, 1993)

   4.3.3 -       Amendment No. 3 to the Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference to
                 Exhibit 10.7.3 to the Company's Form 10-K for the fiscal year ended December 31, 1996)

  *5.1   -       Opinion of Griggs & Harrison, P.C.

 *23.1   -       Consent of Ernst & Young LLP

  23.2   -       Consent of Griggs & Harrison, P.C. (included in Exhibit 5.1)

 *23.3   -       Consent of Huddleston & Co., Inc.
---------------                                   

*Filed herewith

ITEM 9.  UNDERTAKINGS

   (a)   The Company hereby undertakes:

    (1)   To file, during any period in which offers or sales are being made, a
post-effective amendment to this Registration Statement:

        (i) To include any prospectus required by section 10(a)(3) of the
   Securities Act of 1933, as amended (the "Securities Act");

       (ii) To reflect in the prospectus any facts or events arising after the
   effective date of the Registration Statement (or the most recent
   post-effective amendment thereof) which, individually or in the aggregate,
   represent a fundamental change in the information set forth in the
   Registration Statement.  Notwithstanding the foregoing, any increase or
   decrease in volume of securities offered (if the total dollar value of
   securities would not exceed that which was registered) and any deviation
   from the low or high end of the estimated maximum offering range may be
   reflected in the form of prospectus filed with the Commission pursuant to
   Rule 424(b) if, in the aggregate, the changes in volume and price represent
   no more than a 20% change in the maximum aggregate offering price set forth
   in the "Calculation of Registration Fee" table in the effective Registration
   Statement.

      (iii) To include any material information with respect to the plan of
   distribution not previously disclosed in the Registration Statement or any
   material change to such information in the Registration Statement;

provided, however, that paragraphs (i) and (ii) above do not apply if the
information required to be included in a post- effective amendment by those
paragraphs is contained in periodic reports filed by the Company pursuant to
Section 13 or Section 15(d) of the Exchange Act that are incorporated by
reference in this Registration Statement.

   (2)   That, for the purpose of determining any liability under the
Securities Act, each such post-effective amendment shall be deemed to be a new
registration statement relating to the securities offered therein, and the
offering of such securities at that time shall be deemed to be the initial bona
fide offering thereof.

   (3)   To remove from registration by means of a post-effective amendment any
of the securities being registered which remain unsold at the termination of the
offering.
   

                                       5
6
   (b)   The Company hereby undertakes that, for purposes of determining any
liability under the Securities Act, each filing of the Company's annual report
pursuant to Section 13(a) or Section 15(d) of the Exchange Act (and, where
applicable, each filing of an employee benefit plan's annual report pursuant to
section 15(d) of the Exchange Act) that is incorporated by reference in the
Registration Statement shall be deemed to be a new registration  statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.

   (h)   Insofar as indemnification for liabilities arising under the
Securities Act may be permitted to directors, officers and controlling persons
of the Company pursuant to the provisions described under Item 6 above, or
otherwise, the Company has been advised that, in the opinion of the Securities
and Exchange Commission, such indemnification is against public policy as
expressed in the Securities Act and is, therefore, unenforceable.  In the event
that a claim for indemnification against such liabilities (other than the
payment by the Company of expenses incurred or paid by a director, officer or
controlling person of the Company in the successful defense of any action, suit
or proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the Company will, unless, in
the opinion of its counsel, the matter has been settled by controlling
precedent, submit to a court of appropriate jurisdiction the question whether
such indemnification by it is against public policy as expressed in the
Securities Act and will be governed by the final adjudication of such issue.

                                       6
7
                                   SIGNATURES

   Pursuant to the requirements of the Securities Act of 1933, Cliffs Drilling
Company certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-8 and has duly caused this
Registration Statement or Amendment to be signed on its behalf by the
undersigned, thereunto duly authorized, in the City of Houston, State of Texas,
on May 21, 1997.

                                 CLIFFS DRILLING COMPANY
                                 
                                 
                                 By: /s/ Douglas E. Swanson                    
                                     ------------------------------------------
                                               Douglas E. Swanson
                                        Chairman of the Board, President 
                                    (Principal Executive Officer), and Director

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement or Amendment has been signed by the following persons in
the capacities and on the dates indicated.
SIGNATURE                                    TITLE                         DATE
             ---------                                    -----                         ----
/s/ Douglas E. Swanson                     Chairman of the Board, President         May  21, 1997
 ---------------------------------          (Principal Executive Officer),                        
     (Douglas E. Swanson)                   and Director                  
                                                                          
 /s/ M. M. Cone                             Director                                 May  21, 1997
 ---------------------------------                                                                
     (M.M. Cone)

 /s/ H. Robert Hirsch                       Director                                 May  21, 1997
 ---------------------------------                                                                
     (H. Robert Hirsch)

 /s/ Donald W. Keller                       Director                                 May  21, 1997
 ---------------------------------                                                                
     (Donald W. Keller)

 /s/ Robert M. McInnes                      Director                                 May  21, 1997
 ---------------------------------                                                                
     (Robert M. McInnes)

 /s/ Joseph E. Reid                         Director                                 May  21, 1997
 ---------------------------------                                                                
     (Joseph E. Reid)

 /s/ John D. Weil                           Director                                 May  21, 1997
 ---------------------------------                                                                
     (John D. Weil)

 /s/ Edward A. Guthrie                      Vice President - Finance                 May  21, 1997
 --------------------------------           (Principal Financial Officer)                                                      
     (Edward A. Guthrie)

 /s/ Cindy B. Taylor                        Vice President - Controller              May  21, 1997
 ---------------------------------          (Principal Accounting Officer)                        
     (Cindy B. Taylor)
7
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                                 EXHIBIT INDEX
EXHIBIT                                                                                                      SEQUENTIALLY
NUMBER                                                                                                      NUMBERED PAGE
------                                                                                                      -------------
4.1   -       Certificate of Incorporation of the Company, as amended (Incorporated by
                 reference to Exhibit 3.1 to the Company's Registration Statement on Form
                 S-1, No. 33-23508)

   4.2   -       Bylaws of the Company (Incorporated by reference to Exhibit 3.2 to the
                 Company's Registration Statement on Form S-1, No. 33-23508)

   4.3   -       Cliffs Drilling Company 1988 Incentive Equity Plan (incorporated by reference
                 to Exhibit 10.8 to the Company's Registration Statement on Form S-1,
                 No. 33-23508)

   4.3.1 -       Amendment No. 1 to the Cliffs Drilling Company 1988 Incentive Equity Plan
                 (incorporated by reference to Exhibit 10.7.1 to the Company's Form 10-K for the fiscal year
                 ended December 31, 1993)

   4.3.2 -       Amendment No. 2 to the Cliffs Drilling Company 1988 Incentive Equity
                 Plan (incorporated by reference to Exhibit 10.7.2 to the Company's Form 10-K for the fiscal
                 year ended December 31, 1993)

   4.3.3 -       Amendment No. 3 to the Cliffs Drilling Company 1988 Incentive Equity Plan
                 (incorporated by reference to Exhibit 10.7.3 to the Company's Form 10-K for the fiscal year
                 ended December 31, 1996)

  *5.1   -       Opinion of Griggs & Harrison, P.C.

 *23.1   -       Consent of Ernst & Young LLP

  23.2   -       Consent of Griggs & Harrison, P.C. (included in Exhibit 5.1)

 *23.3   -       Consent of Huddleston & Co., Inc.
---------------
*Filed herewith

                                      8