<PAGE>
 
     As filed with the Securities and Exchange Commission on June 29, 1998

                                                   Registration No. 333-________
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

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

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

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

                            TRANSOCEAN OFFSHORE INC.
             (Exact name of registrant as specified in its charter)

         DELAWARE                                76-0464968
(State or other jurisdiction of               (I.R.S. Employer
incorporation or organization)               Identification No.)
 
           4 GREENWAY PLAZA                                 
            HOUSTON, TEXAS                         77046    
(Address of Principal Executive Offices)         (Zip Code) 

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

                          EMPLOYEE STOCK PURCHASE PLAN
                            (Full title of the plan)

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

                                 ERIC B. BROWN
                 VICE PRESIDENT, GENERAL COUNSEL AND SECRETARY
                            TRANSOCEAN OFFSHORE INC.
                                4 GREENWAY PLAZA
                             HOUSTON, TEXAS  77046
                    (Name and address of agent for service)

                                 (713) 871-7500
         (Telephone number, including area code, of agent for service)

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

                        CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
============================================================================================================================
                                                                    Proposed           Proposed maximum
                                             Amount to be      maximum offering       aggregate offering        Amount of
Title of securities to be registered          registered      price per share (2)          price (2)         registration fee
----------------------------------------------------------------------------------------------------------------------------
<S>                                         <C>               <C>                    <C>                   <C>
Common Stock, par value $.01 per share           250,000(1)                 $43.63           $10,907,500          $3,218.00
============================================================================================================================
</TABLE>

(1) Plus such additional number of shares as may be issuable by reason of the
    anti-dilution provisions of the Plan.

(2) Estimated pursuant to Rules 457(c) and (h) solely for the purpose of
    computing the registration fee and based upon the average of the high and
    low sales prices reported on the New York Stock Exchange Composite Tape on
    June 25, 1998
================================================================================

<PAGE>
 
                                     PART I


              INFORMATION REQUIRED IN THE SECTION 10(a) PROSPECTUS


     Note: The document(s) containing the information concerning the Employee
Stock Purchase Plan (the "Plan") required by Item 1 of Form S-8 and the
statement of availability of registrant information, Plan information and other
information required by Item 2 of Form S-8 will be sent or given to participants
as specified by Rule 428. In accordance with Rule 428 and the requirements of
Part I of Form S-8, such documents are not being filed with the Securities and
Exchange Commission (the "Commission") either as part of this Registration
Statement or as prospectuses or prospectus supplements pursuant to Rule 424. The
registrant will maintain a file of such documents in accordance with the
provisions of Rule 428. Upon request, the registrant will furnish to the
Commission or its staff a copy of any or all of the documents included in such
file.

                                       2
<PAGE>
 
                                    PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE.

     The following documents, which Transocean Offshore Inc., a Delaware
corporation (the "Company") has filed with the Commission pursuant to the
Securities Exchange Act of 1934, as amended (the "Exchange Act"), are
incorporated in this Registration Statement by reference and shall be deemed to
be a part hereof:

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

               (2) The Company's Quarterly Report on Form 10-Q for the quarter
          ended March 31, 1998; and

               (3) The description of the Company's common stock, par value
          $0.01 per share (the "Common Stock"), contained in the Company's
          Registration Statement on Form 8-A filed on May 12, 1993, as such
          Registration Statement may be further amended from time to time for
          the purpose of updating, changing or modifying such description;

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

          Any statement contained in this Registration Statement, in an
amendment hereto or in a document incorporated by reference herein shall be
deemed to be modified or superseded for purposes of this Registration Statement
to the extent that a statement contained herein or in any subsequently filed
supplement to this Registration Statement or in any document that also is
incorporated by reference herein modifies or supersedes such statement. Any
statement so modified or superseded shall not be deemed, except as so modified
or superseded, to constitute a part of this Registration Statement.

ITEM 4.  DESCRIPTION OF SECURITIES.

          Not applicable.

ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL.

          Not applicable.

ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.

          Article Tenth of the Company's Amended and Restated Certificate of
Incorporation provides that to the fullest extent that the General Corporation
Law of the State of Delaware ("DGCL") permits the limitation or elimination of
the liability of directors, no director of the Company shall be personally
liable to the Company or its stockholders for damages for breach of fiduciary
duty as a director. Notwithstanding the foregoing, a director shall be liable to
the extent provided by applicable law (1) for any breach of the director's duty
of loyalty to the Company or its stockholders, (2) for acts or omissions not in
good faith or which involve intentional misconduct or a knowing violation of
law, (3) for any willful or negligent declaration of an unlawful dividend, stock
purchase or redemption or (4) for any transaction from which the director
derived any improper personal benefit.

          Article Tenth of the Company's Amended and Restated Certificate of
Incorporation provides that the Company shall indemnify each person who was or
is made a party or is threatened to be made a party to or otherwise require


                                      II-1
<PAGE>
 
representation by counsel in connection with any threatened, pending or
completed action, suit or proceeding, by reason of the fact that he is or was a
director or officer of the Company, or, while serving as such, is or was serving
at the request of the Company as a director, officer, employee or agent of
another corporation, partnership, joint venture, trust or other enterprise, or
by reason of any action alleged to have been taken or omitted in such capacity,
to the fullest extent permitted by the laws of the State of Delaware.

          Section 145 of the DGCL authorizes the indemnification of directors
and officers against liability incurred by reason of being a director or officer
and against expenses (including attorney's fees) in connection with defending
any action seeking to establish such liability, in the case of third-party
claims, if the officer or director 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 actions by or in the right of the corporation,
if the officer or director 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 if
such officer or director shall not have been adjudged liable to the corporation,
unless a court otherwise determines. Indemnification is also authorized with
respect to any criminal action or proceeding where the officer or director had
no reasonable cause to believe his conduct was unlawful.

          The Company has purchased directors and officers liability insurance
that would indemnify the directors and officers of the Company against damages
arising out of certain kinds of claims that might be made against them based on
their negligent acts or omissions while acting in their capacity as such.

ITEM 7.  EXEMPTION FROM REGISTRATION CLAIMED.

          Not Applicable.

ITEM 8.  EXHIBITS.

<TABLE>
<CAPTION>
Exhibit
Number                                                  Document Description
-------                                                 --------------------
<C>               <S>    
   *4.1   --      Restated Certificate of Incorporation of the Company, including amendments dated September 3,
                  1996 (incorporated by reference to Exhibit 4(a) to the Company's Registration Statement on Form
                  S-8 (Registration No. 333-12475) dated September 20, 1996)

   *4.2   --      Amendment dated September 3, 1996 to Restated Certificate of Incorporation of the Company
                  to change the Company's name (incorporated by reference to Exhibit 4(b) to the Company's
                  Registration Statement on Form S-8 (Registration No. 333-12475) dated September 20, 1996)

   *4.3   --      Amendment dated September 3, 1996 to Restated Certificate of Incorporation of the Company
                  to increase authorized shares of common stock (incorporated by reference to Exhibit 4(c) to the
                  Company's Registration Statement on Form S-8 (Registration No. 333-12475) dated September
                  20, 1996)

   *4.4   --      By-Laws of the Company (incorporated by reference to Exhibit 3-(2) to the Company's Form
                  10-K for the year ending December 31, 1993)

    4.5   --      Employee Stock Purchase Plan

      5   --      Opinion of Eric B. Brown, Esq.

   23.1   --      Consent of Ernst & Young LLP

   23.2   --      Consent of Eric B. Brown, Esq. (included in Exhibit 5)

     24   --      Powers of Attorney

</TABLE>
-------------------
*  Incorporated by reference as indicated.

                                      II-2
<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 of 1933;

               (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;

               (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 information required to be included in a post-effective amendment
       by those paragraphs is contained in periodic reports filed by the
       registrant pursuant to section 13 or section 15(d) of the Securities
       Exchange Act of 1934 that are incorporated by reference in the
       Registration Statement.

          (2) That, for the purpose of determining any liability under the
       Securities Act of 1933, 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.

          (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
registrant's annual report pursuant to section 13(a) or section 15(d) of the
Securities Exchange Act of 1934 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.

          (c) Insofar as indemnification for liabilities arising under the
Securities Act of 1933 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 Securities and
Exchange Commission such indemnification is against public policy as expressed
in the 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 Act and will
be governed by the final adjudication of such issue.

                                      II-3
<PAGE>
 
                                   SIGNATURES

          Pursuant to the requirements of the Securities Act of 1933, the
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 to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, the State of Texas, on June 30, 1998.

                                              TRANSOCEAN OFFSHORE INC.


                                      By: /s/ Robert L. Long
                                         --------------------------------
                                         Robert L. Long,
                                         Senior Vice President


          Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities indicated and on June 30, 1998.

<TABLE>
<CAPTION>
                       SIGNATURE                                                      TITLE
                       ---------                                                      -----
<S>                                                        <C>
               /s/ J. Michael Talbert                           Chairman of the Board and Chief Executive Officer
--------------------------------------------------------
                 J. Michael Talbert
             (Principal Executive Officer)

                 /s/ Robert L. Long                             Senior Vice President, Treasurer and Chief Financial Officer
--------------------------------------------------------
                    Robert L. Long
             (Principal Financial Officer)

              /s/ Barbara S. Koucouthakis                       Vice President and Controller
--------------------------------------------------------
                Barbara S. Koucouthakis
             (Principal Accounting Officer)

                          *                                     Director, President and Chief Operating Officer
--------------------------------------------------------
                  W. Dennis Heagney

                                                                Director
--------------------------------------------------------
                  Richard D. Kinder

                          *                                     Director
--------------------------------------------------------
                 Ronald L. Kuehn, Jr.

                                                                Director
--------------------------------------------------------
                  Robert T. Lanigan

                          *                                     Director
--------------------------------------------------------
                 Fridtjof Lorentzen

                          *                                     Director
--------------------------------------------------------
                    Max L. Lukens

                          *                                     Director
--------------------------------------------------------
                  Martin B. McNamara

                          *                                     Director
--------------------------------------------------------
                    Kristian Siem

*By:             /s/ Eric B. Brown
     ----------------------------------------------------
                   Eric B. Brown
                  Attorney in Fact
</TABLE>

                                      II-4
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 18912}]
{"company-data": {"conformed-name": "TRANSOCEAN OFFSHORE INC", "cik": "0000314047", "assigned-sic": "1381", "irs-number": "720464968", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-58203", "film-number": "98658556"}, "business-address": {"street1": "4 GREENWAY PLAZA", "city": "HOUSTON", "state": "TX", "zip": "77046", "phone": "7138717500"}, "mail-address": {"street1": "4 GREENWAY PLAZA", "city": "HOUSTON", "state": "TX", "zip": "77046"}, "former-company": {"former-conformed-name": "SONAT OFFSHORE DRILLING INC", "date-changed": "19930415"}}
As filed with the Securities and Exchange Commission on June 29, 1998

                                                   Registration No. 333-________
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

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

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

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

                            TRANSOCEAN OFFSHORE INC.
             (Exact name of registrant as specified in its charter)

         DELAWARE                                76-0464968
(State or other jurisdiction of               (I.R.S. Employer
incorporation or organization)               Identification No.)
 
           4 GREENWAY PLAZA                                 
            HOUSTON, TEXAS                         77046    
(Address of Principal Executive Offices)         (Zip Code) 

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

                          EMPLOYEE STOCK PURCHASE PLAN
                            (Full title of the plan)

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

                                 ERIC B. BROWN
                 VICE PRESIDENT, GENERAL COUNSEL AND SECRETARY
                            TRANSOCEAN OFFSHORE INC.
                                4 GREENWAY PLAZA
                             HOUSTON, TEXAS  77046
                    (Name and address of agent for service)

                                 (713) 871-7500
         (Telephone number, including area code, of agent for service)

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

                        CALCULATION OF REGISTRATION FEE
============================================================================================================================
                                                                    Proposed           Proposed maximum
                                             Amount to be      maximum offering       aggregate offering        Amount of
Title of securities to be registered          registered      price per share (2)          price (2)         registration fee
----------------------------------------------------------------------------------------------------------------------------
Common Stock, par value $.01 per share           250,000(1)                 $43.63           $10,907,500          $3,218.00
============================================================================================================================
(1) Plus such additional number of shares as may be issuable by reason of the
    anti-dilution provisions of the Plan.

(2) Estimated pursuant to Rules 457(c) and (h) solely for the purpose of
    computing the registration fee and based upon the average of the high and
    low sales prices reported on the New York Stock Exchange Composite Tape on
    June 25, 1998
================================================================================
PART I

              INFORMATION REQUIRED IN THE SECTION 10(a) PROSPECTUS

     Note: The document(s) containing the information concerning the Employee
Stock Purchase Plan (the "Plan") required by Item 1 of Form S-8 and the
statement of availability of registrant information, Plan information and other
information required by Item 2 of Form S-8 will be sent or given to participants
as specified by Rule 428. In accordance with Rule 428 and the requirements of
Part I of Form S-8, such documents are not being filed with the Securities and
Exchange Commission (the "Commission") either as part of this Registration
Statement or as prospectuses or prospectus supplements pursuant to Rule 424. The
registrant will maintain a file of such documents in accordance with the
provisions of Rule 428. Upon request, the registrant will furnish to the
Commission or its staff a copy of any or all of the documents included in such
file.

                                       2
PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE.

     The following documents, which Transocean Offshore Inc., a Delaware
corporation (the "Company") has filed with the Commission pursuant to the
Securities Exchange Act of 1934, as amended (the "Exchange Act"), are
incorporated in this Registration Statement by reference and shall be deemed to
be a part hereof:

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

               (2) The Company's Quarterly Report on Form 10-Q for the quarter
          ended March 31, 1998; and

               (3) The description of the Company's common stock, par value
          $0.01 per share (the "Common Stock"), contained in the Company's
          Registration Statement on Form 8-A filed on May 12, 1993, as such
          Registration Statement may be further amended from time to time for
          the purpose of updating, changing or modifying such description;

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

          Any statement contained in this Registration Statement, in an
amendment hereto or in a document incorporated by reference herein shall be
deemed to be modified or superseded for purposes of this Registration Statement
to the extent that a statement contained herein or in any subsequently filed
supplement to this Registration Statement or in any document that also is
incorporated by reference herein modifies or supersedes such statement. Any
statement so modified or superseded shall not be deemed, except as so modified
or superseded, to constitute a part of this Registration Statement.

ITEM 4.  DESCRIPTION OF SECURITIES.

          Not applicable.

ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL.

          Not applicable.

ITEM 6.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.

          Article Tenth of the Company's Amended and Restated Certificate of
Incorporation provides that to the fullest extent that the General Corporation
Law of the State of Delaware ("DGCL") permits the limitation or elimination of
the liability of directors, no director of the Company shall be personally
liable to the Company or its stockholders for damages for breach of fiduciary
duty as a director. Notwithstanding the foregoing, a director shall be liable to
the extent provided by applicable law (1) for any breach of the director's duty
of loyalty to the Company or its stockholders, (2) for acts or omissions not in
good faith or which involve intentional misconduct or a knowing violation of
law, (3) for any willful or negligent declaration of an unlawful dividend, stock
purchase or redemption or (4) for any transaction from which the director
derived any improper personal benefit.

          Article Tenth of the Company's Amended and Restated Certificate of
Incorporation provides that the Company shall indemnify each person who was or
is made a party or is threatened to be made a party to or otherwise require

                                      II-1
representation by counsel in connection with any threatened, pending or
completed action, suit or proceeding, by reason of the fact that he is or was a
director or officer of the Company, or, while serving as such, is or was serving
at the request of the Company as a director, officer, employee or agent of
another corporation, partnership, joint venture, trust or other enterprise, or
by reason of any action alleged to have been taken or omitted in such capacity,
to the fullest extent permitted by the laws of the State of Delaware.

          Section 145 of the DGCL authorizes the indemnification of directors
and officers against liability incurred by reason of being a director or officer
and against expenses (including attorney's fees) in connection with defending
any action seeking to establish such liability, in the case of third-party
claims, if the officer or director 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 actions by or in the right of the corporation,
if the officer or director 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 if
such officer or director shall not have been adjudged liable to the corporation,
unless a court otherwise determines. Indemnification is also authorized with
respect to any criminal action or proceeding where the officer or director had
no reasonable cause to believe his conduct was unlawful.

          The Company has purchased directors and officers liability insurance
that would indemnify the directors and officers of the Company against damages
arising out of certain kinds of claims that might be made against them based on
their negligent acts or omissions while acting in their capacity as such.

ITEM 7.  EXEMPTION FROM REGISTRATION CLAIMED.

          Not Applicable.

ITEM 8.  EXHIBITS.
Exhibit
Number                                                  Document Description
-------                                                 --------------------
*4.1   --      Restated Certificate of Incorporation of the Company, including amendments dated September 3,
                  1996 (incorporated by reference to Exhibit 4(a) to the Company's Registration Statement on Form
                  S-8 (Registration No. 333-12475) dated September 20, 1996)

   *4.2   --      Amendment dated September 3, 1996 to Restated Certificate of Incorporation of the Company
                  to change the Company's name (incorporated by reference to Exhibit 4(b) to the Company's
                  Registration Statement on Form S-8 (Registration No. 333-12475) dated September 20, 1996)

   *4.3   --      Amendment dated September 3, 1996 to Restated Certificate of Incorporation of the Company
                  to increase authorized shares of common stock (incorporated by reference to Exhibit 4(c) to the
                  Company's Registration Statement on Form S-8 (Registration No. 333-12475) dated September
                  20, 1996)

   *4.4   --      By-Laws of the Company (incorporated by reference to Exhibit 3-(2) to the Company's Form
                  10-K for the year ending December 31, 1993)

    4.5   --      Employee Stock Purchase Plan

      5   --      Opinion of Eric B. Brown, Esq.

   23.1   --      Consent of Ernst & Young LLP

   23.2   --      Consent of Eric B. Brown, Esq. (included in Exhibit 5)

     24   --      Powers of Attorney
-------------------
*  Incorporated by reference as indicated.

                                      II-2
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 of 1933;

               (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;

               (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 information required to be included in a post-effective amendment
       by those paragraphs is contained in periodic reports filed by the
       registrant pursuant to section 13 or section 15(d) of the Securities
       Exchange Act of 1934 that are incorporated by reference in the
       Registration Statement.

          (2) That, for the purpose of determining any liability under the
       Securities Act of 1933, 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.

          (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
registrant's annual report pursuant to section 13(a) or section 15(d) of the
Securities Exchange Act of 1934 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.

          (c) Insofar as indemnification for liabilities arising under the
Securities Act of 1933 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 Securities and
Exchange Commission such indemnification is against public policy as expressed
in the 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 Act and will
be governed by the final adjudication of such issue.

                                      II-3
SIGNATURES

          Pursuant to the requirements of the Securities Act of 1933, the
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 to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, the State of Texas, on June 30, 1998.

                                              TRANSOCEAN OFFSHORE INC.

                                      By: /s/ Robert L. Long
                                         --------------------------------
                                         Robert L. Long,
                                         Senior Vice President

          Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities indicated and on June 30, 1998.
SIGNATURE                                                      TITLE
                       ---------                                                      -----
/s/ J. Michael Talbert                           Chairman of the Board and Chief Executive Officer
--------------------------------------------------------
                 J. Michael Talbert
             (Principal Executive Officer)

                 /s/ Robert L. Long                             Senior Vice President, Treasurer and Chief Financial Officer
--------------------------------------------------------
                    Robert L. Long
             (Principal Financial Officer)

              /s/ Barbara S. Koucouthakis                       Vice President and Controller
--------------------------------------------------------
                Barbara S. Koucouthakis
             (Principal Accounting Officer)

                          *                                     Director, President and Chief Operating Officer
--------------------------------------------------------
                  W. Dennis Heagney

                                                                Director
--------------------------------------------------------
                  Richard D. Kinder

                          *                                     Director
--------------------------------------------------------
                 Ronald L. Kuehn, Jr.

                                                                Director
--------------------------------------------------------
                  Robert T. Lanigan

                          *                                     Director
--------------------------------------------------------
                 Fridtjof Lorentzen

                          *                                     Director
--------------------------------------------------------
                    Max L. Lukens

                          *                                     Director
--------------------------------------------------------
                  Martin B. McNamara

                          *                                     Director
--------------------------------------------------------
                    Kristian Siem

*By:             /s/ Eric B. Brown
     ----------------------------------------------------
                   Eric B. Brown
                  Attorney in Fact
II-4