As filed with the Securities and Exchange Commission on July 7, 1998
                                                  Registration No. 333-_______
_______________________________________________________________________________

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549
                             ----------------------
                                    FORM S-8


            REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
-------------------------------------------------------------------------------

                        ENSCO INTERNATIONAL INCORPORATED
             (Exact name of registrant as specified in its charter)



               Delaware                               76-0232579
    (State or other jurisdiction of      (I.R.S. Employer Identification No.)
     incorporation or organization)


          2700 Fountain Place
           1445 Ross Avenue
             Dallas, Texas                            75202-2792
 (Address of principal executive offices)             (Zip Code)
               
-------------------------------------------------------------------------------

                        ENSCO INTERNATIONAL INCORPORATED
                               1998 INCENTIVE PLAN
                            (Full title of the plan)
-------------------------------------------------------------------------------
                      
                               C. Christopher Gaut
               Vice President-Finance and Chief Financial Officer
                        ENSCO International Incorporated
                               2700 Fountain Place
                                1445 Ross Avenue
                            Dallas, Texas 75202-2792
                                (214) 922-1500
                     (Name and address of agent for service)

                                 with a copy to:

                                 Daniel W. Rabun
                                Baker & McKenzie
                          2001 Ross Avenue, Suite 4500
                               Dallas, Texas 75201

<TABLE>
<CAPTION>


                         CALCULATION OF REGISTRATION FEE


                                                                                 
                                                                                                               
                                                                Proposed maximum          Proposed maximum          Amount of    
Title of securities to                  Amount to               offering price            aggregate offering        registration 
be registered      <F1>                 be registered           per share <F2>            price <F2>                fee          
--------------------------------        -----------------       ----------------          ------------------        ------------   
                                   
<S>                                     <C>                     <C>                        <C>                        <C>   
Common Stock, par value                                                                     
$.10 per Share                          11,300,000 Shares         $ 17.40625                $ 196,690,625             $ 58,024
                  
Preferred Share                                                                                                    
Purchase Rights <F3>                    11,300,000 Rights             N/A                         N/A                    N/A
_________________________________________________________________________________________________________________________________   
<FN>

<F1>  Shares  of  common  stock  of  ENSCO   International   Incorporated   (the
      "Company"),  par  value  $.10 per share  (including  the  preferred  share
      purchase rights attaching thereto,  the "Common Stock"),  being registered
      hereby relate to the ENSCO International  Incorporated 1998 Incentive Plan
      (the "Plan"). Pursuant to Rule 416(c) promulgated under the Securities Act
      of  1933,  as  amended  (the  "Securities  Act"),  there  are  also  being
      registered such  additional  shares of Common Stock as may become issuable
      pursuant to the anti-dilution provisions of the Plan.
<F2>  Estimated  solely for the  purpose of  calculating  the  registration  fee
      pursuant to Rule 457(c) and (h)  promulgated  under the  Securities Act on
      the basis of the  average  of the high and low sale  prices of the  Common
      Stock on June 29, 1998, as reported on the New York Stock Exchange.
<F3>  In accordance with Rule 457(g), no additional registration fee is required
      in respect of preferred share purchase rights.

                                      

</FN>
</TABLE>

                                    



<PAGE>


                                     PART II

                     INFORMATION NOT REQUIRED IN PROSPECTUS

Item 3.     Incorporation of Documents by Reference.

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

     (a)  The Company's  Annual Report on Form 10-K, as amended,  for the fiscal
          year ended December 31, 1997;

     (b)  The Company's  Proxy  Statement filed with the Securities and Exchange
          Commission (the "Commission") dated March 27, 1998;

     (c)  The Company's Quarterly Report on Form 10-Q for the three months ended
          March 31, 1998;

     (d)  The  description  of the  Company's  Common  Stock as contained in the
          Company's Registration Statement on Form 8-B filed with the Commission
          on November 12, 1987, and the Registration Statement on Form 8-A filed
          with the  Commission on February 3, 1981,  each as amended,  including
          all  amendments  and reports  filed for the  purpose of updating  such
          description; and

     (e)  The  description of the Company's  Preferred  Share Purchase Rights as
          contained in the  Company's  Registration  Statement on Form 8-A filed
          with the  Commission on February 23, 1995,  as amended,  including all
          amendments  and  reports  filed  for  the  purpose  of  updating  such
          description.

Item 4. Description of Securities.

        Not  Applicable.

Item 5. Interest of Named Experts and Counsel.

        None.

Item 6. Indemnification of Directors and Officers.


      Section  145  of the  DGCL  provides  that  a  director  or  officer  of a
corporation  (i) shall be  indemnified  by the  corporation  for all expenses of
litigation or other legal  proceedings  brought against such person by reason of
the fact that such person is or was a director or an officer of the  corporation
when he is successful on the merits,  (ii) may be indemnified by the corporation
for the  expenses,  judgments,  fines,  and amounts paid in  settlement  of such
litigation  (other than a derivative  suit) even if he is not  successful on the
merits if he acted in good faith and in a manner he reasonably believed to be in
or not opposed to the best interests of the  corporation  (and, in the case of a
criminal  proceeding,  had no reason to believe his conduct was  unlawful),  and
(iii) may be indemnified by the corporation for expenses of a derivative suit (a
suit by a stockholder  alleging a breach by a director or officer of a duty owed
to the corporation),  even if he is not successful on the merits, if he acted in
good faith and in a manner he reasonably believed to be in or not opposed to the
best interests of the corporation,  provided that no such indemnification may be
made in accordance with this clause (iii) if the director or officer is adjudged
liable  to the  corporation,  unless  a  court  determines  that,  despite  such
adjudication  but in view of all  circumstances,  he is  fairly  and  reasonably
entitled to indemnification of such expenses.  The indemnification  described in
clauses  (ii) and (iii)  above  shall be made  only  upon  order by a court or a
determination by (a) a majority of directors who are not parties to such action,
(b) a majority vote of a committee  consisting of such disinterested  directors,
(c)  independent  legal  counsel in a written  opinion if no such  disinterested
directors  exist,  or if such  disinterested  directors  so  direct,  or (d) the
stockholders,  that indemnification is proper because the applicable standard of
conduct is met.  Expenses  incurred  by a director  or officer in  defending  an
action may be advanced by the corporation prior to the final disposition of such
action upon receipt of an  undertaking by such director or officer to repay such
expenses  if  it  is  ultimately  determined  that  he  is  not  entitled  to be
indemnified in connection with the proceeding to which the expenses relate.
<PAGE>

      Article 15 of the Company's  Certificate  of  Incorporation  provides,  in
general,  that the Company must  indemnify  its  directors  and  officers  under
certain of the  circumstances  defined in Section  145 of the DGCL,  and that no
director  of the  Company  will  be  personally  liable  to the  Company  or its
stockholders  for monetary  damages for any breach of such director's  fiduciary
duty, with certain exceptions. Article 15 further allows the Company to purchase
and maintain insurance on behalf of the Company's directors, officers, employees
or agents  and to provide  for such  indemnification  by means of a trust  fund,
security  interest,  letter of credit,  surety  bond,  contract  and/or  similar
arrangement.  The directors and officers of the Company and its subsidiaries are
insured (subject to certain exceptions and deductions) against liabilities which
they may  incur in their  capacity  as such,  including  liabilities  under  the
Securities Act, under a liability  insurance policy carried by the Company.  The
Company has also entered into  agreements  with its officers and directors which
essentially  provide that the Company will  indemnify the officers and directors
to the  extent  set forth in the  Company's  Certificate  of  Incorporation  and
Bylaws.

      Article VII,  Section 7 of the Company's  Bylaws  provide that the Company
must  indemnify  its  officers,  directors,  employees and agents to the fullest
extent permitted by the DGCL.

Item 7. Exemption from Registration Claimed.

        None.

Item 8. Exhibits.

        The following are filed as exhibits to this Registration Statement:

Exhibit No.       Description
-----------       -----------

  4.1             ENSCO International Incorporated 1998 Incentive Plan.*

  4.2             Amended   and   Restated    Certificate    of    Incorporation
                  (incorporated  by reference to Exhibit 3.1 to the Registrant's
                  Quarterly  Report on Form 10-Q for the quarter  ended June 30,
                  1997, File No. 1-8097).

  4.3             Bylaws  of  the  Company,   as  amended   (incorporated   by
                  reference to Exhibit 3.2 to the  Registrant's  Annual Report
                  on Form 10-K for the year ended December 31, 1992,  File No.
                  1-8097).

  4.4             Rights Agreement, dated February 21, 1995, between the Company
                  and American Stock Transfer & Trust Company,  as Rights Agent,
                  which  includes  as  Exhibit  A the  Form  of  Certificate  of
                  Designations of Series A Junior Participating  Preferred Stock
                  of ENSCO International Incorporated,  as Exhibit B the Form of
                  Right  Certificate,  and as Exhibit C the Summary of Rights to
                  Purchase  Shares  of  Preferred  Stock of ENSCO  International
                  Incorporated  (incorporated  by  reference  to  Exhibit  4  to
                  Registrant's  Form  8-K  dated  February  21,  1995,  File No.
                  1-8097).

  4.5             First  Amendment  to Rights  Agreement,  dated  March 3, 1997,
                  between ENSCO  International  Incorporated  and American Stock
                  Transfer & Trust  Company,  as Rights Agent  (incorporated  by
                  reference to Exhibit 4.2 to the Registrant's Current Report on
                  Form 8-K dated March 3, 1997, File No. 1-8097).

  4.6             Certificate of  Designation  of Series A Junior  Participating
                  Preferred Stock of the Company  (incorporated  by reference to
                  Exhibit 4.6 to the  Registrant's  Annual Report on Form 10-K/A
                  for the year ended December 31, 1995, File No. 1-8097).
                  
  5.1             Opinion of Baker & McKenzie*

 23.1             Consent of Baker & McKenzie (see Exhibit 5.1)*

 23.2             Consent of Independent Accountants*

 24.1             Power of Attorney  (included  on the  signature  page of the
                  Registration Statement)*

----------------
* filed herewith
<PAGE>

Item 9.  Undertakings.

      (a)   The undersigned Registrant 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;

            (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 this
      Registration  Statement.  Notwithstanding  the foregoing,  any increase or
      decrease in volume of  securities  offered (if the total  dollar  value of
      securities  offered  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 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 (a)(1)(i) and (a)(1)(ii) do not apply if the
Registration Statement is on Form S-3, Form S-8 or Form F-3, and the information
required to be included in a  post-effective  amendment by those  paragraphs  is
contained in periodic  reports filed with or furnished to the  Commission by the
Registrant  pursuant to Section 13 or Section 15(d) of the Exchange Act that are
incorporated by reference in the 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  herein,  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.

      (b) The undersigned  Registrant  hereby  undertakes  that, for purposes of
determining  any  liability  under  the  Securities  Act,  each  filing  of  the
Registrant'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 herein, and the
offering of such  securities at that time shall be deemed to be the initial bona
fide offering thereof.

      (c)  Insofar  as  indemnification   for  liabilities   arising  under  the
Securities Act may be permitted to directors,  officers and controlling  persons
of the  Registrant  pursuant to the  foregoing  provisions,  or  otherwise,  the
Registrant  has  been  advised  that  in  the  opinion  of the  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 Registrant of expenses
incurred or paid by a director,  officer or controlling person of the Registrant
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 Registrant 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.




<PAGE>


                                   SIGNATURES
      Pursuant  to  the  requirements  of the  Securities  Act,  the  Registrant
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  to be  signed  on its  behalf  by  the  undersigned,  thereunto  duly
authorized, in the City of Dallas, State of Texas, on June 30, 1998.



                                      ENSCO INTERNATIONAL INCORPORATED





                                      By: /s/ Carl F.Thorne 
                                          ------------------------------------
                                              Carl F. Thorne
                                              Chairman of the Board, President
                                              and Chief Executive Officer


                                POWER OF ATTORNEY
      Each person  whose  signature  appears  below  hereby  authorizes  Carl F.
Thorne,  Richard A. Wilson and C. Christopher Gaut, and each of them, any one of
whom may act  without  joinder  of the  others,  to file one or more  amendments
(including  post-effective  amendments) to this  registration  statement,  which
amendments may make such changes in this registration  statement as each of them
deems appropriate,  and each such person hereby appoints Carl F. Thorne, Richard
A. Wilson and C.  Christopher  Gaut,  and each of them,  any one of whom may act
without the joinder of the others,  attorney-in-fact  to execute in the name and
on behalf of the Company and any such person,  individually and in each capacity
stated below, any such amendments to this registration statement.

      Pursuant to the  requirements of the Securities  Act, this  registration
statement has been signed by the following  persons in the  capacities  and on
the date indicated.


           Signature                   Title                       Date
           ---------                   -----                       ----


    /s/ Carl F. Thorne         Chairman of the Board,           June 30, 1998
    -----------------------    President and Chief Executive    
        Carl F. Thorne         Officer(Principal Executive   
                               Officer)                      
                               

    /s/ Richard A. Wilson      Director,Senior Vice             June 30, 1998
    -----------------------    President and Chief Operating    
        Richard A. Wilson      Officer                       
                               

    /s/ C. Christopher Gaut    Vice President--Finance and      June 30, 1998
    -----------------------    Chief Financial Officer          
        C. Christopher Gaut    (Principal Financial Officer) 
                               
 
    /s/ H. E. Malone           Vice President-Controller and    June 30, 1998
    -----------------------    Chief Accounting Officer         
        H. E. Malone           (Principal Accounting Officer)
                                                             
                               
    /s/ Craig I. Fields        Director                         June 30, 1998
    -----------------------    
        Craig I. Fields

    
    /s/ Orville D.Gaither,Sr.  Director                         June 30, 1998
    -----------------------                            
        Orville D.Gaither,Sr.

    
    /s/ Gerald W. Haddock      Director                         June 30, 1998
    -----------------------    
        Gerald W. Haddock
    
<PAGE>
    
    /s/ Dillard S. Hammett     Director                         June 30, 1998
    -----------------------   
        Dillard S. Hammett
    
      
    /s/ Thomas L. Kelly II     Director                         June 30, 1998
    -----------------------    
        Thomas L. Kelly II

  
    /s/ Morton H. Meyerson     Director                         June 30, 1998
    -----------------------    
        Morton H. Meyerson



                                  EXHIBIT INDEX

Exhibit No.       Description
-----------       -----------

  4.1             ENSCO International Incorporated 1998 Incentive Plan.*

  4.2             Amended   and   Restated    Certificate    of    Incorporation
                  (incorporated  by reference to Exhibit 3.1 to the Registrant's
                  Quarterly  Report on Form 10-Q for the quarter  ended June 30,
                  1997, File No. 1-8097).

  4.3             Bylaws  of  the  Company,   as  amended   (incorporated   by
                  reference to Exhibit 3.2 to the  Registrant's  Annual Report
                  on Form 10-K for the year ended December 31, 1992,  File No.
                  1-8097).

  4.4             Rights Agreement, dated February 21, 1995, between the Company
                  and American Stock Transfer & Trust Company,  as Rights Agent,
                  which  includes  as  Exhibit  A the  Form  of  Certificate  of
                  Designations of Series A Junior Participating  Preferred Stock
                  of ENSCO International Incorporated,  as Exhibit B the Form of
                  Right  Certificate,  and as Exhibit C the Summary of Rights to
                  Purchase  Shares  of  Preferred  Stock of ENSCO  International
                  Incorporated  (incorporated  by  reference  to  Exhibit  4  to
                  Registrant's  Form  8-K  dated  February  21,  1995,  File No.
                  1-8097).

  4.5             First  Amendment  to Rights  Agreement,  dated  March 3, 1997,
                  between ENSCO  International  Incorporated  and American Stock
                  Transfer & Trust  Company,  as Rights Agent  (incorporated  by
                  reference to Exhibit 4.2 to the Registrant's Current Report on
                  Form 8-K dated March 3, 1997, File No. 1-8097).

  4.6             Certificate of  Designation  of Series A Junior  Participating
                  Preferred Stock of the Company  (incorporated  by reference to
                  Exhibit 4.6 to the  Registrant's  Annual Report on Form 10-K/A
                  for the year ended December 31, 1995, File No.1-8097).

  5.1             Opinion of Baker & McKenzie*

 23.1             Consent of Baker & McKenzie (see Exhibit 5.1)*

 23.2             Consent of Independent Accountants*

 24.1             Power of Attorney  (included  on the  signature  page of the
                  Registration Statement)*

----------------
* filed herewith
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 24551}]
{"company-data": {"conformed-name": "ENSCO INTERNATIONAL INC", "cik": "0000314808", "assigned-sic": "1381", "irs-number": "760232579", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-58625", "film-number": "98661340"}, "business-address": {"street1": "2700 FOUNTAIN PL", "street2": "1445 ROSS AVE STE 2700", "city": "DALLAS", "state": "TX", "zip": "75202-2792", "phone": "2149221500"}, "mail-address": {"street1": "2700 FOUNTAIN PLACE", "street2": "1445 ROSS AVE", "city": "DALLAS", "state": "TX", "zip": "75202-2792"}, "former-company": [{"former-conformed-name": "ENERGY SERVICE COMPANY INC", "date-changed": "19920703"}, {"former-conformed-name": "BLOCKER ENERGY CORP", "date-changed": "19871015"}]}
As filed with the Securities and Exchange Commission on July 7, 1998
                                                  Registration No. 333-_______
_______________________________________________________________________________

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549
                             ----------------------
                                    FORM S-8

            REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
-------------------------------------------------------------------------------

                        ENSCO INTERNATIONAL INCORPORATED
             (Exact name of registrant as specified in its charter)

               Delaware                               76-0232579
    (State or other jurisdiction of      (I.R.S. Employer Identification No.)
     incorporation or organization)

          2700 Fountain Place
           1445 Ross Avenue
             Dallas, Texas                            75202-2792
 (Address of principal executive offices)             (Zip Code)
               
-------------------------------------------------------------------------------

                        ENSCO INTERNATIONAL INCORPORATED
                               1998 INCENTIVE PLAN
                            (Full title of the plan)
-------------------------------------------------------------------------------
                      
                               C. Christopher Gaut
               Vice President-Finance and Chief Financial Officer
                        ENSCO International Incorporated
                               2700 Fountain Place
                                1445 Ross Avenue
                            Dallas, Texas 75202-2792
                                (214) 922-1500
                     (Name and address of agent for service)

                                 with a copy to:

                                 Daniel W. Rabun
                                Baker & McKenzie
                          2001 Ross Avenue, Suite 4500
                               Dallas, Texas 75201
CALCULATION OF REGISTRATION FEE

                                                                                 
                                                                                                               
                                                                Proposed maximum          Proposed maximum          Amount of    
Title of securities to                  Amount to               offering price            aggregate offering        registration 
be registered
be registered           per share
price
fee          
--------------------------------        -----------------       ----------------          ------------------        ------------
Common Stock, par value                                                                     
$.10 per Share                          11,300,000 Shares         $ 17.40625                $ 196,690,625             $ 58,024
                  
Preferred Share                                                                                                    
Purchase Rights
11,300,000 Rights             N/A                         N/A                    N/A
_________________________________________________________________________________________________________________________________
Shares  of  common  stock  of  ENSCO   International   Incorporated   (the
      "Company"),  par  value  $.10 per share  (including  the  preferred  share
      purchase rights attaching thereto,  the "Common Stock"),  being registered
      hereby relate to the ENSCO International  Incorporated 1998 Incentive Plan
      (the "Plan"). Pursuant to Rule 416(c) promulgated under the Securities Act
      of  1933,  as  amended  (the  "Securities  Act"),  there  are  also  being
      registered such  additional  shares of Common Stock as may become issuable
      pursuant to the anti-dilution provisions of the Plan.
Estimated  solely for the  purpose of  calculating  the  registration  fee
      pursuant to Rule 457(c) and (h)  promulgated  under the  Securities Act on
      the basis of the  average  of the high and low sale  prices of the  Common
      Stock on June 29, 1998, as reported on the New York Stock Exchange.
In accordance with Rule 457(g), no additional registration fee is required
      in respect of preferred share purchase rights.
PART II

                     INFORMATION NOT REQUIRED IN PROSPECTUS

Item 3.     Incorporation of Documents by Reference.

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

     (a)  The Company's  Annual Report on Form 10-K, as amended,  for the fiscal
          year ended December 31, 1997;

     (b)  The Company's  Proxy  Statement filed with the Securities and Exchange
          Commission (the "Commission") dated March 27, 1998;

     (c)  The Company's Quarterly Report on Form 10-Q for the three months ended
          March 31, 1998;

     (d)  The  description  of the  Company's  Common  Stock as contained in the
          Company's Registration Statement on Form 8-B filed with the Commission
          on November 12, 1987, and the Registration Statement on Form 8-A filed
          with the  Commission on February 3, 1981,  each as amended,  including
          all  amendments  and reports  filed for the  purpose of updating  such
          description; and

     (e)  The  description of the Company's  Preferred  Share Purchase Rights as
          contained in the  Company's  Registration  Statement on Form 8-A filed
          with the  Commission on February 23, 1995,  as amended,  including all
          amendments  and  reports  filed  for  the  purpose  of  updating  such
          description.

Item 4. Description of Securities.

        Not  Applicable.

Item 5. Interest of Named Experts and Counsel.

        None.

Item 6. Indemnification of Directors and Officers.

      Section  145  of the  DGCL  provides  that  a  director  or  officer  of a
corporation  (i) shall be  indemnified  by the  corporation  for all expenses of
litigation or other legal  proceedings  brought against such person by reason of
the fact that such person is or was a director or an officer of the  corporation
when he is successful on the merits,  (ii) may be indemnified by the corporation
for the  expenses,  judgments,  fines,  and amounts paid in  settlement  of such
litigation  (other than a derivative  suit) even if he is not  successful on the
merits if he acted in good faith and in a manner he reasonably believed to be in
or not opposed to the best interests of the  corporation  (and, in the case of a
criminal  proceeding,  had no reason to believe his conduct was  unlawful),  and
(iii) may be indemnified by the corporation for expenses of a derivative suit (a
suit by a stockholder  alleging a breach by a director or officer of a duty owed
to the corporation),  even if he is not successful on the merits, if he acted in
good faith and in a manner he reasonably believed to be in or not opposed to the
best interests of the corporation,  provided that no such indemnification may be
made in accordance with this clause (iii) if the director or officer is adjudged
liable  to the  corporation,  unless  a  court  determines  that,  despite  such
adjudication  but in view of all  circumstances,  he is  fairly  and  reasonably
entitled to indemnification of such expenses.  The indemnification  described in
clauses  (ii) and (iii)  above  shall be made  only  upon  order by a court or a
determination by (a) a majority of directors who are not parties to such action,
(b) a majority vote of a committee  consisting of such disinterested  directors,
(c)  independent  legal  counsel in a written  opinion if no such  disinterested
directors  exist,  or if such  disinterested  directors  so  direct,  or (d) the
stockholders,  that indemnification is proper because the applicable standard of
conduct is met.  Expenses  incurred  by a director  or officer in  defending  an
action may be advanced by the corporation prior to the final disposition of such
action upon receipt of an  undertaking by such director or officer to repay such
expenses  if  it  is  ultimately  determined  that  he  is  not  entitled  to be
indemnified in connection with the proceeding to which the expenses relate.
Article 15 of the Company's  Certificate  of  Incorporation  provides,  in
general,  that the Company must  indemnify  its  directors  and  officers  under
certain of the  circumstances  defined in Section  145 of the DGCL,  and that no
director  of the  Company  will  be  personally  liable  to the  Company  or its
stockholders  for monetary  damages for any breach of such director's  fiduciary
duty, with certain exceptions. Article 15 further allows the Company to purchase
and maintain insurance on behalf of the Company's directors, officers, employees
or agents  and to provide  for such  indemnification  by means of a trust  fund,
security  interest,  letter of credit,  surety  bond,  contract  and/or  similar
arrangement.  The directors and officers of the Company and its subsidiaries are
insured (subject to certain exceptions and deductions) against liabilities which
they may  incur in their  capacity  as such,  including  liabilities  under  the
Securities Act, under a liability  insurance policy carried by the Company.  The
Company has also entered into  agreements  with its officers and directors which
essentially  provide that the Company will  indemnify the officers and directors
to the  extent  set forth in the  Company's  Certificate  of  Incorporation  and
Bylaws.

      Article VII,  Section 7 of the Company's  Bylaws  provide that the Company
must  indemnify  its  officers,  directors,  employees and agents to the fullest
extent permitted by the DGCL.

Item 7. Exemption from Registration Claimed.

        None.

Item 8. Exhibits.

        The following are filed as exhibits to this Registration Statement:

Exhibit No.       Description
-----------       -----------

  4.1             ENSCO International Incorporated 1998 Incentive Plan.*

  4.2             Amended   and   Restated    Certificate    of    Incorporation
                  (incorporated  by reference to Exhibit 3.1 to the Registrant's
                  Quarterly  Report on Form 10-Q for the quarter  ended June 30,
                  1997, File No. 1-8097).

  4.3             Bylaws  of  the  Company,   as  amended   (incorporated   by
                  reference to Exhibit 3.2 to the  Registrant's  Annual Report
                  on Form 10-K for the year ended December 31, 1992,  File No.
                  1-8097).

  4.4             Rights Agreement, dated February 21, 1995, between the Company
                  and American Stock Transfer & Trust Company,  as Rights Agent,
                  which  includes  as  Exhibit  A the  Form  of  Certificate  of
                  Designations of Series A Junior Participating  Preferred Stock
                  of ENSCO International Incorporated,  as Exhibit B the Form of
                  Right  Certificate,  and as Exhibit C the Summary of Rights to
                  Purchase  Shares  of  Preferred  Stock of ENSCO  International
                  Incorporated  (incorporated  by  reference  to  Exhibit  4  to
                  Registrant's  Form  8-K  dated  February  21,  1995,  File No.
                  1-8097).

  4.5             First  Amendment  to Rights  Agreement,  dated  March 3, 1997,
                  between ENSCO  International  Incorporated  and American Stock
                  Transfer & Trust  Company,  as Rights Agent  (incorporated  by
                  reference to Exhibit 4.2 to the Registrant's Current Report on
                  Form 8-K dated March 3, 1997, File No. 1-8097).

  4.6             Certificate of  Designation  of Series A Junior  Participating
                  Preferred Stock of the Company  (incorporated  by reference to
                  Exhibit 4.6 to the  Registrant's  Annual Report on Form 10-K/A
                  for the year ended December 31, 1995, File No. 1-8097).
                  
  5.1             Opinion of Baker & McKenzie*

 23.1             Consent of Baker & McKenzie (see Exhibit 5.1)*

 23.2             Consent of Independent Accountants*

 24.1             Power of Attorney  (included  on the  signature  page of the
                  Registration Statement)*

----------------
* filed herewith
Item 9.  Undertakings.

      (a)   The undersigned Registrant 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;

            (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 this
      Registration  Statement.  Notwithstanding  the foregoing,  any increase or
      decrease in volume of  securities  offered (if the total  dollar  value of
      securities  offered  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 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 (a)(1)(i) and (a)(1)(ii) do not apply if the
Registration Statement is on Form S-3, Form S-8 or Form F-3, and the information
required to be included in a  post-effective  amendment by those  paragraphs  is
contained in periodic  reports filed with or furnished to the  Commission by the
Registrant  pursuant to Section 13 or Section 15(d) of the Exchange Act that are
incorporated by reference in the 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  herein,  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.

      (b) The undersigned  Registrant  hereby  undertakes  that, for purposes of
determining  any  liability  under  the  Securities  Act,  each  filing  of  the
Registrant'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 herein, and the
offering of such  securities at that time shall be deemed to be the initial bona
fide offering thereof.

      (c)  Insofar  as  indemnification   for  liabilities   arising  under  the
Securities Act may be permitted to directors,  officers and controlling  persons
of the  Registrant  pursuant to the  foregoing  provisions,  or  otherwise,  the
Registrant  has  been  advised  that  in  the  opinion  of the  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 Registrant of expenses
incurred or paid by a director,  officer or controlling person of the Registrant
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 Registrant 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.
SIGNATURES
      Pursuant  to  the  requirements  of the  Securities  Act,  the  Registrant
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  to be  signed  on its  behalf  by  the  undersigned,  thereunto  duly
authorized, in the City of Dallas, State of Texas, on June 30, 1998.

                                      ENSCO INTERNATIONAL INCORPORATED

                                      By: /s/ Carl F.Thorne 
                                          ------------------------------------
                                              Carl F. Thorne
                                              Chairman of the Board, President
                                              and Chief Executive Officer

                                POWER OF ATTORNEY
      Each person  whose  signature  appears  below  hereby  authorizes  Carl F.
Thorne,  Richard A. Wilson and C. Christopher Gaut, and each of them, any one of
whom may act  without  joinder  of the  others,  to file one or more  amendments
(including  post-effective  amendments) to this  registration  statement,  which
amendments may make such changes in this registration  statement as each of them
deems appropriate,  and each such person hereby appoints Carl F. Thorne, Richard
A. Wilson and C.  Christopher  Gaut,  and each of them,  any one of whom may act
without the joinder of the others,  attorney-in-fact  to execute in the name and
on behalf of the Company and any such person,  individually and in each capacity
stated below, any such amendments to this registration statement.

      Pursuant to the  requirements of the Securities  Act, this  registration
statement has been signed by the following  persons in the  capacities  and on
the date indicated.

           Signature                   Title                       Date
           ---------                   -----                       ----

    /s/ Carl F. Thorne         Chairman of the Board,           June 30, 1998
    -----------------------    President and Chief Executive    
        Carl F. Thorne         Officer(Principal Executive   
                               Officer)                      
                               

    /s/ Richard A. Wilson      Director,Senior Vice             June 30, 1998
    -----------------------    President and Chief Operating    
        Richard A. Wilson      Officer                       
                               

    /s/ C. Christopher Gaut    Vice President--Finance and      June 30, 1998
    -----------------------    Chief Financial Officer          
        C. Christopher Gaut    (Principal Financial Officer) 
                               
 
    /s/ H. E. Malone           Vice President-Controller and    June 30, 1998
    -----------------------    Chief Accounting Officer         
        H. E. Malone           (Principal Accounting Officer)
                                                             
                               
    /s/ Craig I. Fields        Director                         June 30, 1998
    -----------------------    
        Craig I. Fields

    
    /s/ Orville D.Gaither,Sr.  Director                         June 30, 1998
    -----------------------                            
        Orville D.Gaither,Sr.

    
    /s/ Gerald W. Haddock      Director                         June 30, 1998
    -----------------------    
        Gerald W. Haddock
/s/ Dillard S. Hammett     Director                         June 30, 1998
    -----------------------   
        Dillard S. Hammett
    
      
    /s/ Thomas L. Kelly II     Director                         June 30, 1998
    -----------------------    
        Thomas L. Kelly II

  
    /s/ Morton H. Meyerson     Director                         June 30, 1998
    -----------------------    
        Morton H. Meyerson

                                  EXHIBIT INDEX

Exhibit No.       Description
-----------       -----------

  4.1             ENSCO International Incorporated 1998 Incentive Plan.*

  4.2             Amended   and   Restated    Certificate    of    Incorporation
                  (incorporated  by reference to Exhibit 3.1 to the Registrant's
                  Quarterly  Report on Form 10-Q for the quarter  ended June 30,
                  1997, File No. 1-8097).

  4.3             Bylaws  of  the  Company,   as  amended   (incorporated   by
                  reference to Exhibit 3.2 to the  Registrant's  Annual Report
                  on Form 10-K for the year ended December 31, 1992,  File No.
                  1-8097).

  4.4             Rights Agreement, dated February 21, 1995, between the Company
                  and American Stock Transfer & Trust Company,  as Rights Agent,
                  which  includes  as  Exhibit  A the  Form  of  Certificate  of
                  Designations of Series A Junior Participating  Preferred Stock
                  of ENSCO International Incorporated,  as Exhibit B the Form of
                  Right  Certificate,  and as Exhibit C the Summary of Rights to
                  Purchase  Shares  of  Preferred  Stock of ENSCO  International
                  Incorporated  (incorporated  by  reference  to  Exhibit  4  to
                  Registrant's  Form  8-K  dated  February  21,  1995,  File No.
                  1-8097).

  4.5             First  Amendment  to Rights  Agreement,  dated  March 3, 1997,
                  between ENSCO  International  Incorporated  and American Stock
                  Transfer & Trust  Company,  as Rights Agent  (incorporated  by
                  reference to Exhibit 4.2 to the Registrant's Current Report on
                  Form 8-K dated March 3, 1997, File No. 1-8097).

  4.6             Certificate of  Designation  of Series A Junior  Participating
                  Preferred Stock of the Company  (incorporated  by reference to
                  Exhibit 4.6 to the  Registrant's  Annual Report on Form 10-K/A
                  for the year ended December 31, 1995, File No.1-8097).

  5.1             Opinion of Baker & McKenzie*

 23.1             Consent of Baker & McKenzie (see Exhibit 5.1)*

 23.2             Consent of Independent Accountants*

 24.1             Power of Attorney  (included  on the  signature  page of the
                  Registration Statement)*

----------------
* filed herewith