TRANSOCEAN OFFSHORE INC /NEW/
POS AM, 1999-06-29
DRILLING OIL & GAS WELLS
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<PAGE>


     As filed with the Securities and Exchange Commission on June 28, 1999
                                                    Registration No. 333 - 24457
================================================================================
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549
                         ----------------------------
                                POST-EFFECTIVE
                                AMENDMENT NO. 1
                                      TO
                                   FORM S-3
                            REGISTRATION STATEMENT
                                     Under
                          THE SECURITIES ACT OF 1993
                         ----------------------------
                           TRANSOCEAN OFFSHORE INC.
            (Exact name of registrant as specified in its charter)


        CAYMAN ISLANDS              4 GREENWAY PLAZA               N/A
(State or other jurisdiction of   HOUSTON, TEXAS 77046      (I.R.S. Employer
incorporation or organization)       (713) 871-7500         Identification No.)
                             (Address, including zip code,
                            and telephone number, including
                 area code, of registrant's principal  executive offices)

                              NICOLAS J. EVANOFF
                           TRANSOCEAN OFFSHORE INC.
                               4 GREENWAY PLAZA
                             HOUSTON, TEXAS 77046
                                (713) 232-7500
               (Name, address, including zip code, and telephone
              number, including area code, of agent for service)
                         ----------------------------
                                 WITH COPY TO:
                                GENE J. OSHMAN
                             BAKER & BOTTS, L.L.P.
                             3000 ONE SHELL PLAZA
                             HOUSTON, TEXAS 77002
                                (713) 229-1234

     APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC:  From
time to time after the effective date of this Registration Statement.
     If the only securities being registered on this Form are to be offered
pursuant to dividend or interest reinvestment plans, please check the following
box.  [_]
     If any of the securities being registered on this Form are to be
offered on a delayed or continuous basis pursuant to Rule 415 under the
Securities Act of 1933, as amended (the "Securities Act"), other than securities
offered only in connection with dividend or interest reinvestment plans, check
the following box.  [X]
     If this Form is filed to register additional securities for an
offering pursuant to Rule 462(b) under the Securities Act, please check the
following box and list the Securities Act registration statement number of the
earlier effective registration statement  for the same offering.  [_]
     If this Form is a post-effective amendment filed pursuant to Rule
462(c) under the Securities Act, check the following box and list the Securities
Act registration statement number of the earlier effective registration
statement for the same offering.  [_]
     If delivery of the prospectus is expected to be made pursuant to Rule 434,
please check the following box. [_]

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

<TABLE>
<CAPTION>
                                                  CALCULATION OF REGISTRATION FEE
============================================================================================================================
                                                                       Proposed            Proposed
                 Title of                              Amount          Maximum            Maximum
         Each Class of Securities                      to be        Offering Price        Aggregate             Amount of
             to be Registered                        Registered      Per Unit (1)     Offering Price (2)    Registration Fee
- ----------------------------------------------------------------------------------------------------------------------------
<S>                                              <C>               <C>               <C>                  <C>
Debt Securities(3)...............................
- ----------------------------------------------------------------------------------------------------------------------------
Preference Shares, par value $.10 per share(4)...
- ----------------------------------------------------------------------------------------------------------------------------
Warrants(5)......................................
- ----------------------------------------------------------------------------------------------------------------------------
Ordinary Shares, par value $.01 per share(6).....
- ----------------------------------------------------------------------------------------------------------------------------
   Total.........................................   $750,000,000(7)      100%           $750,000,000         $227,273(7)
============================================================================================================================
</TABLE>
(1)  The proposed maximum initial offering price per unit will be determined
     from time to time by the Registrant.
(2)  Estimated solely for the purpose of calculating the registration fee
     pursuant to Rule 457(o).  In no event will the aggregate initial offering
     price of all securities issued from time to time pursuant to this
     Registration Statement exceed $750,000,000 or the equivalent thereof in
     foreign currencies.  Any securities registered hereunder may be sold
     separately or as units with other securities registered hereunder.
(3)  Subject to Footnote (2), there is being registered hereunder an
     indeterminate principal amount of Debt Securities that may be issued from
     time to time by the Registrant, including Debt Securities issuable upon
     conversion or exchange of Debt Securities or Preference Shares or upon
     exercise of Warrants. If any such Debt Securities are issued at an original
     issue discount, then the offering price shall be in such greater principal
     amount as shall result in an aggregate initial offering price of up to
     $750,000,000.
(4)  Subject to Footnote (2), there is being registered hereunder an
     indeterminate number of Preference Shares that may be issued from time to
     time by the Registrant, including Preference Shares issuable upon
     conversion or exchange of Debt Securities or Preference Shares or upon
     exercise of Warrants.
(5)  Subject to Footnote (2), there is being registered hereunder an
     indeterminate principal amount of Warrants to purchase Debt Securities or
     Preference Shares.
(6)  Subject to Footnote (2), there is being registered hereunder an
     indeterminate number of Ordinary Shares that may be issued from time to
     time by the Registrant, including Ordinary Shares issuable upon conversion
     or exchange of Debt Securities or Preference Shares.
(7)  Previously paid.

     This Post-Effective Amendment is being filed pursuant to Rule 414 under the
Securities Act by Transocean Offshore Inc., a Cayman Islands exempted company
("Transocean-Cayman" or the "Company" ), as successor to Transocean Offshore
Inc., a Delaware corporation ("Transocean-Delaware").  Transocean-Cayman hereby
expressly adopts the Registration Statement of Transocean-Delaware on Form S-3
(Registration No. 333-24457) as its own Registration Statement for all purposes
of the Securities Act and the Securities Exchange Act of 1934, as amended (the
"Exchange Act").

     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(A) OF
THE SECURITIES ACT OF 1933, OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING PURSUANT TO SAID SECTION 8(A),
MAY DETERMINE.

================================================================================

<PAGE>



                               EXPLANATORY NOTE

     In Transocean-Delaware's Registration Statement on Form S-3 (Registration
No. 333-24457) declared effective on April 11, 1997 (the "Registration
Statement"), Transocean-Delaware registered the sale of Securities (as defined
therein) with an aggregate initial offering price not to exceed $750,000,000,
$450,000,000 of which remain unsold at the date of filing of this Post-Effective
Amendment No. 1 to the Registration Statement. Accordingly, the prospectus
included herein contemplates the issuance of Securities with an aggregate
initial offering price not to exceed $450,000,000.

<PAGE>


++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ The information in this prospectus is not complete and may be changed.  We   +
+ may not sell these securities until the registration statement filed with the+
+ Securities and Exchange Commission is effective. This prospectus is not an   +
+ offer to sell these securities, and it is not soliciting an offer to buy     +
+ these securities in any state where the offer or sale is not permitted.      +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

                  SUBJECT TO COMPLETION, DATED JUNE 28, 1999

PROSPECTUS


                                 $450,000,000


                      [Logo of Transocean Offshore Inc.]



                                DEBT SECURITIES
                               PREFERENCE SHARES
                                ORDINARY SHARES
                                   WARRANTS



     We may offer from time to time our

     .   unsecured debt securities, which may be either senior or subordinated
         and may be convertible into or exchangeable for our preference shares,
         ordinary shares or other debt securities
     .   preference shares, which may be convertible into or exchangeable for
         our debt securities, ordinary shares or other preference shares
     .   ordinary shares, and
     .   warrants to purchase debt securities or preference shares

     The aggregate initial offering price of the securities that we offer will
not exceed $450,000,000. We will offer the securities in amounts, at prices and
on terms to be determined at the time of our offering. We will provide the
specific terms of the securities in supplements to this prospectus. You should
read this prospectus and any supplement carefully before you invest.



     NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR DETERMINED WHETHER
THIS PROSPECTUS IS TRUTHFUL OR COMPLETE. ANY REPRESENTATION TO THE CONTRARY IS A
CRIMINAL OFFENSE.



                The date of this prospectus is ______ __, 1999

<PAGE>


                               TABLE OF CONTENTS

About This Prospectus.......................................................  2

Forward-Looking Statements..................................................  2

About Transocean Offshore Inc...............................................  3

Where You Can Find More Information.........................................  3

Use of Proceeds.............................................................  4

Ratio of Earnings to Fixed Charges..........................................  4

Description of Debt Securities..............................................  4

Description of Capital Stock................................................ 14

Description of Ordinary Shares.............................................. 14

Description of Preference Shares............................................ 17

Description of Warrants..................................................... 18

Anti-takeover Provisions.................................................... 19

Plan of Distribution........................................................ 20

Legal Opinions.............................................................. 21

Experts..................................................................... 22


                             ABOUT THIS PROSPECTUS

     This prospectus is part of a registration statement that we have filed with
the Securities and Exchange Commission under a "shelf" registration process.
This prospectus provides you with a general description of the securities we may
offer.  Each time we offer securities, we will provide a prospectus supplement
and, if applicable, a pricing supplement.  The prospectus supplement and any
pricing supplement will describe the specific terms of that offering, the
offered securities, any material United States federal income tax consequences
and other special considerations.  The prospectus supplement and any pricing
supplement may also add to, update or change the information contained in this
prospectus.  Please carefully read this prospectus, the prospectus supplement
and any pricing supplement, in addition to the information contained in the
documents we refer to under the heading "Where You Can Find More Information."

                          FORWARD-LOOKING STATEMENTS

     This prospectus includes or incorporates by reference forward-looking
statements that reflect our current view of future events and financial
performance.  These forward-looking statements are subject to numerous risks and
uncertainties, including those factors discussed elsewhere in or incorporated by
reference into this prospectus, any prospectus supplement and our other filings
with the SEC.

     These risks and uncertainties could cause actual results or events to
differ materially from historical results or those anticipated.  You can
identify forward-looking statements by the use of words like "anticipate,"
"believe," "budget," "estimate," "expect," "forecast," "intend," "plan,"
"predict," "project" and similar expressions. Any statement that is not a
historical fact is a forward-looking statement. We caution you not to place
undue reliance on these forward-looking statements, which speak only as of their
dates. We undertake no obligation to publicly update or revise any forward-
looking statements, whether as a result of new information, future events or
otherwise.


                                       2
<PAGE>


                        ABOUT TRANSOCEAN OFFSHORE INC.

     We are a leading international provider of deepwater and harsh environment
contract drilling services for oil and gas wells.  As of June 1, 1999, we owned,
had partial ownership in or managed 30 mobile offshore drilling rigs.  On that
date, our fleet consisted of seven fourth-generation semisubmersibles, fourteen
second- and third-generation semisubmersibles, three drillships, including one
newbuild drillship, the "Discoverer Enterprise," which is currently undergoing
sea trials, and six jackup rigs.  We also have under construction two additional
Discoverer Enterprise-class drillships, to be named "Discoverer Spirit" and
"Discoverer Deep Seas."  We contract these drilling rigs, related equipment and
work crews primarily on a dayrate basis to drill offshore wells.  We also
provide additional drilling services, including turnkey drilling, coiled tubing
drilling and well intervention, and management of third-party well service
activities.  Our principal executive offices are located at 4 Greenway Plaza,
Houston, Texas 77046, and our telephone number at that location is (713) 232-
7500.

     As used in this prospectus, "we" means Transocean Offshore Inc., a Cayman
Islands exempted company, and its subsidiaries, unless the context indicates
otherwise.

                      WHERE YOU CAN FIND MORE INFORMATION

     We file annual, quarterly and current reports, proxy statements and other
information with the SEC.  You can read and copy these materials at the SEC's
public reference room at 450 Fifth Street, N.W., Washington, D.C. 20549 and at
the SEC's regional offices located at Seven World Trade Center, New York, New
York 10048 and at 500 West Madison Street, 14th Floor, Chicago, Illinois 60661.
You can obtain information about the operation of the SEC's public reference
room by calling the SEC at 1-800-SEC-0330.  The SEC also maintains a Web site
that contains information we file electronically with the SEC, which you can
access over the Internet at http://www.sec.gov.  You can obtain information
about us at the offices of the New York Stock Exchange, 20 Broad Street, New
York, New York 10005.

     This prospectus is part of a registration statement we have filed with the
SEC relating to the securities.  As permitted by SEC rules, this prospectus does
not contain all of the information we have included in the registration
statement and the accompanying exhibits and schedules.  You may refer to the
registration statement, exhibits and schedules for more information about us and
our securities. The registration statement, exhibits and schedules are available
at the SEC's public reference room or through its Web site.

     The SEC allows us to "incorporate by reference" the information we file
with them, which means that we can disclose important information to you by
referring you to those documents.  The information we incorporate by reference
is an important part of this prospectus, and later information that we file with
the SEC will automatically update and supersede this information.  We
incorporate by reference the documents listed below and any future filings we
make with the SEC under Sections 13(a), 13(c), 14 or 15(d) of the Securities
Exchange Act of 1934 until we sell all the offered securities.  In this
prospectus, we refer to our predecessor Transocean Offshore Inc., a Delaware
corporation, as Transocean-Delaware and to our predecessor Transocean Offshore
(Texas) Inc., a Texas corporation, as Transocean-Texas.  The documents we
incorporate by reference are:

     .   Transocean-Delaware's Annual Report on Form 10-K for the year ended
         December 31, 1998

     .   Transocean-Delaware's Quarterly Report on Form 10-Q for the quarter
         ended March 31, 1999

     .   Transocean-Delaware's Current Report on Form 8-K dated March 15, 1999

     .   our Current Report on Form 8-K dated May 14, 1999, and

     .   the description of our ordinary shares contained in our Current Report
         on Form 8-K dated May 14, 1999

                                       3
<PAGE>


     You may request a copy of these filings (other than an exhibit to those
filings unless we have specifically incorporated that exhibit by reference into
the filing), at no cost, by writing or telephoning us at the following address:

          Transocean Offshore Inc.
          4 Greenway Plaza
          Houston, Texas 77046
          Attention:   Director of Investor Relations
          Telephone: (713) 232-7500

     You should rely only on the information contained or incorporated by
reference in this prospectus or any prospectus supplement.  We have not
authorized any person (including any salesman or broker) to provide information
other than that provided in this prospectus or any prospectus supplement.  We
have not authorized anyone to provide you with different information.  We are
not making an offer of these securities in any state where the offer is not
permitted.  You should not assume that the information in this prospectus or any
prospectus supplement is accurate as of any date other than the date on its
cover page.

                                USE OF PROCEEDS

     Unless we inform you otherwise in the prospectus supplement, we will use
the net proceeds from the sale of the offered securities for general corporate
purposes.  These purposes may include repayment or refinancing of indebtedness,
working capital, capital expenditures, acquisitions and repurchases and
redemptions of securities.  Pending any specific application, we may initially
invest funds in short-term marketable securities or apply them to the reduction
of short-term indebtedness.

                      RATIO OF EARNINGS TO FIXED CHARGES

     Our ratio of earnings to fixed charges for each of the periods shown is as
follows:

                          Three Months Ended
                              March 31,        Year Ended December 31,
                             ----------   --------------------------------
                             1999  1998   1998   1997   1996   1995   1994
                             ----  ----   ----   ----   ----   ----   ----
Ratio of earnings to fixed
  charges.................   9.4    8.3    8.4    5.1   11.1   24.4    8.3

     We have computed the ratios of earnings to fixed charges shown above by
dividing earnings available for fixed charges by fixed charges.  For this
purpose, "earnings available for fixed charges" consist of earnings before
income taxes plus fixed charges less capitalized interest and undistributed
equity in earnings (losses) of joint ventures.  "Fixed charges" consist of
interest expense, capitalized interest and the portion of rental expense that
represents the interest factor.

                        DESCRIPTION OF DEBT SECURITIES

     We may issue two types of debt securities, senior or subordinated.  When we
issue them, we will file a prospectus supplement describing the exact terms of
the debt securities.  The senior debt securities will be issued under an
indenture with Chase Bank of Texas, N.A., as trustee, that was dated April 15,
1997 and has since been supplemented.  The subordinated debt securities will be
issued under an indenture that will be entered into with a trustee and will be
described in the prospectus supplement for those debt securities.  We sometimes
call the senior indenture and the subordinated indenture the indentures.  We
have summarized selected provisions of the debt securities and the indentures
below.  The summary is not complete.  For a complete description, you should
refer to the indentures and the terms of the debt securities, which we have
filed or which we will file with the SEC.  Please read "Where You Can Find More
Information."

                                       4
<PAGE>


     The indentures do not limit the amount of debt securities we can issue and
do not limit the amount of other indebtedness we may incur.  We may issue debt
securities under the indentures from time to time in separate series, each up to
the aggregate amount we authorize from time to time for that series.

     The indentures do not contain any covenants or other provisions designed to
protect holders of the debt securities in the event of a highly leveraged
transaction.  The indentures also do not contain provisions that give holders of
the debt securities the right to require us to repurchase their securities in
the event of a decline in our credit rating resulting from a takeover,
recapitalization or similar restructuring or otherwise.

     The prospectus supplement relating to any series of debt securities being
offered will include specific terms relating to the offering.  These terms will
include some or all of the following:

     .   the title of the debt securities

     .   the total principal amount of the debt securities

     .   whether the debt securities are senior debt securities or subordinated
         debt securities

     .   whether we will issue the debt securities in individual certificates to
         each holder or in the form of temporary or permanent global securities
         held by a depository on behalf of holders

     .   the date or dates on which the principal of and any premium on the
         debt securities will be payable

     .   any interest rate, the date from which interest will accrue, interest
         payment dates and record dates for interest payments

     .   whether and under what circumstances any additional amounts with
         respect to the debt securities will be payable

     .   the place or places where payments on the debt securities will be
         payable

     .   any optional redemption provisions

     .   any sinking fund or other provisions that would obligate us to redeem,
         purchase or repay debt securities

     .   the denominations in which debt securities will be issuable

     .   whether payments on the debt securities will be payable in foreign
         currency or currency units or another form and whether payments will be
         payable by reference to any index or formula

     .   the portion of the principal amount of debt securities that will be
         payable if the maturity is accelerated, if other than the entire
         principal amount

     .   any additional means of defeasance of the debt securities and any
         additional conditions to defeasance of the debt securities

     .   any changes or additions to events of default or covenants

     .   any restrictions or other provisions relating to the transfer or
         exchange of debt securities

     .   any terms for the conversion or exchange of the debt securities for
         our preference shares, ordinary shares or other debt securities

     .   any other terms of the debt securities

                                       5
<PAGE>


     We may sell the debt securities at a discount (which may be substantial)
below their stated principal amount.  These debt securities may bear no interest
or interest at a rate that at the time of issuance is below market rates.

     If we sell any of the debt securities for any foreign currency or currency
unit or if payments on the debt securities are payable in any foreign currency
or currency unit, we will describe in the prospectus supplement the
restrictions, elections, tax consequences, specific terms and other information
relating to those debt securities and the foreign currency or currency unit.

RANKING

     The debt securities will be our unsecured obligations. The senior debt
securities will rank equal in right of payment with all of our other unsecured
and unsubordinated indebtedness. The subordinated debt securities will rank in
right of payment below any senior debt securities and below our other senior
debt. For a more detailed description of the subordination of the subordinated
debt securities, see "--Provisions Applicable Solely to Subordinated Debt
Securities."

     The indentures do not limit the amount of debt that we or any of our
subsidiaries may incur or issue, nor do they restrict transactions between us
and our affiliates or dividends and other distributions by us or our
subsidiaries.

     We conduct a substantial portion of our operations through subsidiaries,
and a substantial portion of our operating income and cash flow is generated by
our subsidiaries.  As a result, distributions or advances from our subsidiaries
are important sources of funds necessary to meet our debt service obligations.
Contractual provisions or laws, as well as our subsidiaries' financial condition
and operating requirements, may limit our ability to obtain from our
subsidiaries the cash we need to pay our debt service obligations, including
payments on the debt securities.  In addition, holders of the debt securities
will have a junior position to the claims of creditors of our subsidiaries on
their assets and earnings.

EVENTS OF DEFAULT

     Unless we inform you otherwise in the prospectus supplement, the following
are events of default with respect to a series of debt securities:

     .   our failure to pay interest on or any additional amounts with respect
         to any debt securities of that series for 30 days

     .   our failure to pay principal of or any premium on any debt securities
         of that series when due

     .   our failure to make any sinking fund payment for that series of debt
         securities for 30 days

     .   our failure to perform any of our other covenants in the indenture
         (other than a covenant included in the indenture solely for the
         benefit of another series of debt securities) for 90 days after
         written notice by the trustee or by the holders of at least 25% in
         principal amount of all outstanding debt securities under that
         indenture

     .   various events involving our bankruptcy, insolvency or
         reorganization, and

     .   any other event of default provided for that series of debt
         securities

     A default under one series of debt securities will not necessarily be a
default under another series.  The trustee may withhold notice to the holders of
the debt securities of any default or event of default (except in any payment on
the debt securities) if the trustee considers it in the interest of the holders
of the debt securities to do so.

     If an event of default for any series of debt securities occurs and is
continuing, the trustee or the holders of at least 25% in principal amount of
the outstanding debt securities of the series affected by the default (or, in
some cases, of all outstanding debt securities under that indenture, voting as
one class) may declare the principal of those

                                       6
<PAGE>


debt securities to be due and payable immediately. If an event of default
relating to events of bankruptcy, insolvency or reorganization occurs, the
principal of all the debt securities will become immediately due and payable
without any action on the part of the trustee or any holder. The holders of a
majority in principal amount of the outstanding debt securities of the series
affected by the default (or, in some cases, of all outstanding debt securities
under that indenture, voting as one class) may in some cases rescind this
accelerated payment requirement. Depending on the terms of our other
indebtedness, an event of default under the indentures may give rise to cross
defaults on our other indebtedness.

     A holder of a debt security of any series may pursue any remedy under the
indenture only if:

     .   the holder has previously given written notice to the trustee of a
         continuing event of default with respect to that series of debt
         securities

     .   the holders of not less than 25% in principal amount of the
         outstanding debt securities of that series have made written request
         to the trustee to institute proceedings in its own name

     .   the holder has offered the trustee reasonable indemnity

     .   the trustee has failed to act within 60 days after receipt of the
         notice and indemnity, and

     .   the holders of a majority in principal amount of the outstanding debt
         securities of that series have given no direction inconsistent with
         the request

This provision does not, however, affect the right of a holder of any debt
security to sue for the enforcement of any overdue payment.

     In most cases, the trustee will be under no obligation to exercise any of
its rights or powers under the indenture at the request or direction of any of
the holders, unless those holders have offered to the trustee reasonable
indemnity.  The holders of a majority in principal amount of the outstanding
debt securities of any series (or, in some cases, of all outstanding debt
securities under the indenture) may direct the time, method and place of:

     .   conducting any proceeding for any remedy available to the trustee, or

     .   exercising any trust or power conferred on the trustee with respect
         to the debt securities of that series

     If an event of default occurs and is continuing, the trustee will be
required to use the degree of care and skill of a prudent man in the conduct of
his own affairs.

     We are required to furnish to the trustee annually a statement as to our
performance of certain of our obligations under the indenture and as to any
default in performance.

CONSOLIDATION, MERGER AND SALE OF ASSETS

     The indentures generally permit a consolidation or merger between us and
another entity.  The indentures also permit our transfer or disposal of all or
substantially all of our assets.  We have agreed, however, that we will
consolidate with or merge into any entity, or transfer or dispose all or
substantially all of our assets to any entity, only if:

     .   the resulting entity assumes the due and punctual payments of the
         debt securities issued under the indentures and the performance of our
         covenants under the indentures, and

     .   immediately after giving effect to the transaction, no event of
         default, and no event that, after notice or lapse of time, would
         become an event of default, would occur and be continuing

                                       7
<PAGE>


If a resulting person assumes the debt securities and the indentures as
described above, we will be relieved of our obligations under the debt
securities and indentures, except in the case of our transfer or disposal of
assets by lease.

DEFEASANCE

     When we use the term "defeasance," we mean discharge from some or all of
our obligations under the applicable indenture.  If we deposit with the trustee
money or U.S. government securities sufficient to make payments on the debt
securities of a series on the dates those payments are due and payable, then at
our option either of the following will occur:

     .   we will no longer have any obligation to comply with the restrictive
         covenants under the indenture, and the related events of default will
         no longer apply to us, but our other obligations under the indenture
         and the debt securities of that series will survive ("covenant
         defeasance"), including our obligations to make payments on the debt
         securities, to register the transfer or exchange of debt securities of
         that series, to replace stolen, lost or mutilated debt securities of
         that series, to maintain paying agencies and to hold monies for payment
         in trust, or

     .   if permitted by the terms of that series of debt securities, we will be
         discharged from all of our obligations with respect to the debt
         securities of that series ("legal defeasance and discharge") and
         holders of debt securities of that series would be entitled to look
         only to the trust fund for payments on their debt securities

     Unless we inform you otherwise in the prospectus supplement, we will be
required to deliver to the trustee an opinion of counsel that the deposit and
related defeasance would not cause the holders of the debt securities to
recognize income, gain or loss for federal income tax purposes.  If we elect
legal defeasance and discharge, that opinion of counsel must be based upon a
ruling from the United States Internal Revenue Service or a change in law to
that effect.

PAYMENT AND PAYING AGENTS

     Unless we inform you otherwise in the prospectus supplement, we will make
payments on the debt securities at the office of the paying agents we designate
from time to time.  We may make, at our option, interest payments by check
mailed to the person entitled to the payment as it appears on the security
register.  Unless we inform you otherwise in a prospectus supplement, we will
make interest payments to the person in whose name the debt security is
registered at the close of business on the record date for the interest payment.

     We have designated the corporate trust office of the trustee as a paying
agent for payments on the senior debt securities.  We may at any time designate
additional paying agents, rescind the designation of any paying agent or approve
a change in the office through which any paying agent acts.  We will, however,
be required to maintain a paying agent in each place of payment for a series of
debt securities.

     Any funds we pay to a paying agent for payments on any debt security that
remain unclaimed for three years after the payments become due and payable will
be repaid to us, subject to applicable escheat laws.  After repayment to us, the
holder of that debt security must look only to us for payment and not to the
paying agent.

MODIFICATION AND WAIVER

     We may modify or amend the indenture if the holders of a majority in
principal amount of the outstanding debt securities of all series issued under
the indenture (acting as one class) affected by the modification or amendment
consent to it.  Without the consent of the holder of each outstanding debt
security affected, however, no modification may:

     .   change the stated maturity of the principal of or any installment of
         principal of or interest on any debt security

                                       8
<PAGE>


     .   reduce the principal amount of, the interest rate on, any additional
         amount with respect to or the premium payable upon redemption of any
         debt security

     .   change the subordination provisions of the subordinated indenture in
         a manner that is adverse to the holders of subordinated debt
         securities

     .   make the debt security payable in a currency other than originally
         stated in the debt security

     .   change the place where the principal of, any additional amounts with
         respect to or any premium or interest on any debt security is payable

     .   impair the right to institute suit for the enforcement of any payment
         on any debt security

     .   reduce the percentage in principal amount of outstanding debt
         securities necessary to modify the indenture, waive compliance with
         the provisions of such indenture or waive defaults, or

     .   modify any of the above provisions

     We and the trustee may agree to modify, amend or supplement the indenture
without the consent of any holders of the debt securities in certain
circumstances, including:

     .   to provide for the assumption of our obligations under the indenture
         and the debt securities by our successor upon any merger,
         consolidation or sale or other transfer of assets

     .   to add covenants and events of default or to change or surrender any
         of our rights under the indenture

     .   to provide security for any series of debt securities

     .   to make any change that does not adversely affect any outstanding
         debt securities of a series

     .   to cure any ambiguity, defect or inconsistency

     .   to establish the terms of any series of debt securities

     .   to add provisions necessary to permit or facilitate covenant
         defeasance of any series of debt securities if we have received an
         opinion of counsel that those provisions do not materially adversely
         affect the holders of any series of debt securities

     .   to provide for successor trustees

     The holders of a majority in principal amount of the outstanding debt
securities of any series (or, in some cases, of all outstanding debt securities
under the indenture or of all series affected) may waive past defaults under the
indenture and compliance by us with our covenants under the indenture.  Those
holders may not, however, waive any default in any payment on any debt security
of that series or compliance with a provision that cannot be modified or amended
without the consent of each holder affected.

FORM, EXCHANGE, REGISTRATION AND TRANSFER

     We will issue the debt securities in registered form. Debt securities of
any series will be exchangeable for other debt securities of the same series,
the same total principal amount and the same terms, but in different authorized
denominations in accordance with the indenture. Holders may present debt
securities for registration of transfer at the office of the security registrar
or any transfer agent we designate. The security registrar or transfer agent
will effect the transfer or exchange when the registrar or agent is satisfied
with the documents of title and identity of the person making the request. We
will not charge a service charge for any registration of transfer or

                                       9
<PAGE>


exchange of the debt securities. We may, however, require the payment of any tax
or other governmental charge payable for that registration.

     We have appointed the trustee as security registrar for the senior debt
securities.  We will appoint the trustee under the subordinated indenture as the
security registrar for the subordinated debt securities, unless we indicate
otherwise in the prospectus supplement.  We are required to maintain an office
or agency for transfers and exchanges in each place of payment.  We may at any
time designate additional transfer agents for any series of debt securities or
rescind the designation of any transfer agent.

     In the case of any redemption in part, we will not be required:

     .   to issue, register the transfer of or exchange debt securities of a
         series during a period beginning 15 days before the day of mailing of
         the relevant notice of redemption and ending on the close of business
         on the day of mailing of the relevant notice of redemption, or

     .   to register the transfer or exchange of any debt security, or portion
         of any debt security, selected for redemption, except the unredeemed
         portion of any debt security we are redeeming in part

REPLACEMENT OF DEBT SECURITIES

     We will replace at the holder's expense any mutilated debt security upon
surrender of the debt security to the trustee.  We will replace at the holder's
expense debt securities that become destroyed, stolen or lost upon delivery to
the trustee of the debt security or evidence of destruction, loss or theft
satisfactory to us and the trustee.  In the case of a destroyed, lost or stolen
debt security, we may require an indemnity at the holder's expense satisfactory
to the trustee and to us before we issue a replacement debt security.

BOOK-ENTRY DEBT SECURITIES

     We may issue the debt securities of a series in the form of one or more
global debt securities that would be deposited with a depositary or its nominee
identified in the prospectus supplement.  We may issue global debt securities in
either temporary or permanent form.  We will describe in the prospectus
supplement the terms of any depositary arrangement and the rights and
limitations of owners of beneficial interests in any global debt security.  The
prospectus supplement will also describe the form, exchange, registration and
transfer of debt securities we may issue in temporary or permanent global forms.

MEETINGS

     Meetings may be convened on notice:

     .   by the trustee

     .   by us, if we ask the trustee to call a meeting and it fails to do so,
         or

     .   by the holders of 10% in principal amount of the debt securities of a
         series, if they ask the trustee to call a meeting and it fails to do
         so

     Holders entitled to vote a majority in principal amount of the outstanding
debt securities of a series constitute a quorum at any meeting.  Except for
actions requiring the consent of all holders of debt securities affected by the
action, any action at a meeting adopted by the holders of a majority in
principal amount of the debt securities of any series (or a lesser percentage
required for the action by the indenture) will be binding on all holders of the
debt securities of that series.

NOTICES

     Notices to holders of debt securities will be given by mail to the holder's
address as it appears in the security register.

                                       10
<PAGE>


GOVERNING LAW

     New York law governs the indentures and the debt securities.

THE TRUSTEE

     Chase Bank of Texas, N.A. is the trustee under the senior indenture.  We
may borrow money and maintain other banking relationships, in the ordinary
course of business, with any trustee and its affiliates under any indenture.
The indentures, however, contain limitations on the right of the trustee, if it
becomes one of our creditors, to obtain payment of claims or to realize on
certain property received for any such claim, as security or otherwise.  If the
trustee acquires any conflicting interest, it must eliminate that conflict or
resign.

PROVISIONS APPLICABLE SOLELY TO SENIOR DEBT SECURITIES

     The following provisions are included in the senior indenture and apply to
any series of senior debt securities, unless we indicate otherwise in the
prospectus supplement.  In the following discussion, when we refer to our
"drilling rigs and drillships," we mean any drilling rig or drillship (or the
stock or indebtedness of any subsidiary owning such a drilling rig or drillship)
that we lease or own all or part of and that our board of directors deems of
material importance to us and that has a gross book value greater than 2% of
consolidated net tangible assets.  When we refer to "consolidated net tangible
assets," we mean the total amount of our assets (less reserves and other
properly deductible items) after deducting current liabilities (other than those
that are extendable at our option to a date more than 12 months after the date
the amount is determined), goodwill and other intangible assets shown in our
most recent consolidated balance sheet prepared in accordance with GAAP.

     Limitation on Liens

     In the senior indenture, we have agreed that we will not create, assume or
allow to exist any debt secured by a lien upon any of our drilling rigs or
drillships, unless  we secure each series of senior debt securities equally and
ratably with the debt secured by the lien.  This covenant has exceptions that
permit:

     .   liens already existing on the date the applicable series of senior
         debt securities are issued

     .   liens on property existing at the time we acquire the property or liens
         on property of a corporation or other entity at the time it becomes a
         subsidiary

     .   liens securing debt incurred to finance the acquisition, completion of
         construction and commencement of commercial operation, alteration,
         repair or improvement of any property, if the debt was incurred prior
         to, at the time of or within 12 months after that event, and to the
         extent that debt is in excess of the purchase price or cost, recourse
         on the debt is only against that property

     .   liens securing intercompany debt

     .   liens in favor of a governmental entity to secure either:

         (1) payments under any contract or statute, or

         (2) industrial development, pollution control or similar indebtedness

     .   liens imposed by law such as mechanic's or workmen's liens

     .   governmental liens under contracts for the sale of products or services

     .   liens under workers compensation laws or similar legislation

     .   liens in connection with legal proceedings or securing taxes or
         assessments

                                       11
<PAGE>


     .   good faith deposits in connection with bids, tenders, contracts or
         leases

     .   deposits made in connection with maintaining self-insurance, to obtain
         the benefits of laws, regulations or arrangements relating to
         unemployment insurance, old age pensions, social security or similar
         matters or to secure surety, appeal or customs bonds, and

     .   any extensions, renewals or replacements of the above-described liens
         if both:

         (1) the amount of debt secured by the new lien does not exceed the
             amount of debt secured, plus any additional debt used to complete
             the project, and

         (2) the new lien is limited to all or a part of the property (plus
             any improvements) secured by the original lien

     In addition, without securing the senior debt securities as described
above, we may create, assume or allow to exist secured debt that this covenant
would otherwise restrict in an aggregate amount that does not exceed a "basket"
equal to 10% of our consolidated net tangible assets.  When determining whether
secured debt is permitted by this exception, we must include in the calculation
of the "basket" amount all of our other secured debt that this covenant would
otherwise restrict and the present value of lease payments in connection with
sale and lease-back transactions that would be prohibited by the "Limitation on
Sale and Lease-Back Transactions"covenant described below if this exception did
not apply.

     Limitation on Sale and Lease-Back Transactions

     We have agreed that we will not enter into a sale and lease-back
transaction covering any drilling rig or drillship, unless one of the following
applies:

     .   we could incur debt secured by the leased property in an amount at
         least equal to the present value of the lease payments in connection
         with that sale and lease-back transaction without violating the
         "Limitation on Liens" covenant described above, or

     .   within six months of the effective date of the sale and lease-back
         transaction, we apply an amount equal to the present value of the lease
         payments in connection with the sale and lease-back transaction to
         either:

         (1) the acquisition of any drilling rig or drillship, or

         (2) the retirement (by redemption, defeasement, repurchase or
             otherwise) of long-term debt or other debt maturing more than one
             year after its creation, in each case ranking equally with the
             debt securities

     When we use the term "sale and lease-back transaction," we mean any
arrangement by which we sell or transfer to any person any drilling rig or
drillship that we then lease back from them.  This term excludes leases shorter
than three years, intercompany leases, leases executed within 12 months of the
acquisition, construction, improvement or commencement of commercial operation
of the drilling rig or drillship, and arrangements pursuant to any provision of
law with an effect similar to the former Section 168(f)(8) of the Internal
Revenue Code of 1954 (which permitted the lessor to recognize depreciation on
the property).

PROVISIONS APPLICABLE SOLELY TO SUBORDINATED DEBT SECURITIES

     Under the subordinated indenture, payment of the principal, interest, any
additional amounts and any premium on the subordinated debt securities will
generally be subordinated and junior in right of payment to the prior payment in
full of all of our senior debt.  The subordinated indenture provides that we may
not pay principal, interest, any additional amounts or any premium on the
subordinated debt securities, and we may not acquire any subordinated debt
securities (other than for our junior securities), if:

                                       12
<PAGE>


     .   we fail to pay the principal, interest or premium on the senior debt
         when due, or

     .   we default in performing any other covenant (a "covenant default") in
         any senior debt that we designate for this purpose in the instrument
         creating that senior debt, if the covenant default allows the holders
         of that senior debt to accelerate the maturity of the senior debt they
         hold

     A covenant default will only prevent us from paying the subordinated debt
securities for up to 179 days after holders of the senior debt give the trustee
for the subordinated debt securities notice of the covenant default, unless that
senior debt has been declared due and payable in its entirety.

     The subordination does not affect our obligation to pay, when due,
principal, interest, any additional amounts and any premium on the subordinated
debt securities.  In addition, the subordination does not prevent the occurrence
of any default under the subordinated indenture.

     If we distribute our assets or dissolve, liquidate or reorganize in
bankruptcy, insolvency or similar proceedings:

     .   the holders of all of our senior indebtedness will first be entitled to
         receive payment in full before the holders of subordinated debt
         securities are entitled to receive any payment (other than payments of
         our junior securities), and

     .   any payment or distribution of assets (other than our junior
         securities) that the holders of subordinated debt securities or the
         trustee would otherwise be entitled to receive will be paid directly to
         the holders of our senior indebtedness or their representatives, to the
         extent necessary to pay in full all of our senior indebtedness

As a result of the subordination of the subordinated debt securities, if we
distribute our assets, dissolve, liquidate or become insolvent or bankrupt,
holders of subordinated debt securities may receive less on a proportionate
basis than other creditors.

     If the trustee or the holders of subordinated debt securities receive any
payment or distribution of assets (other than our junior securities) that is
prohibited by the foregoing provisions, then the trustee or the holders of
subordinated debt securities will hold those amounts for the benefit of the
holders of our senior indebtedness and will be obligated to pay or deliver those
amounts to the holders of our senior indebtedness or their representatives.

     The subordinated indenture does not limit the amount of senior debt that we
may incur.  Unless we inform you otherwise in the prospectus supplement, "senior
debt" will mean the following types of indebtedness, unless that indebtedness
states that it is not senior to the subordinated debt securities or our other
junior debt:

     .   all of our liabilities and obligations (1) in respect of borrowed
         money, (2) evidenced by bonds, notes, debentures or similar
         instruments, (3) representing the balance of the purchase price of any
         property or services, (4) evidenced by bankers' acceptances or similar
         instruments issued or accepted by banks, (5) for the payment of money
         relating to a capitalized lease obligation or (6) evidenced by a letter
         of credit or a reimbursement obligation with respect to any letter of
         credit

     .   all of our net obligations under interest swap and hedging obligations

     .   all liabilities of others of the kind described in the preceding two
         clauses that we have guaranteed or are otherwise our legal liability

     .   all obligations to purchase, redeem or acquire any of our capital stock
         or rights to purchase our capital stock (other than convertible or
         exchangeable indebtedness), and

     .   all amendments, deferrals, renewals, extensions, refinancings or
         refundings of any liability of the kind described above

                                       13
<PAGE>


However, "senior indebtedness" will not include:

     .   indebtedness to any of our subsidiaries, officers, directors or
         employees

     .   indebtedness to trade creditors, or

     .   any liability for taxes

                         DESCRIPTION OF CAPITAL STOCK

     We are a Cayman Islands company. Our authorized capital stock consists of:

     .   150,000,000 ordinary shares

     .   50,000,000 preference shares

     As of June 15, 1999, there were 100,563,834 ordinary shares outstanding and
no preference shares outstanding.

     The following description of our ordinary shares and preference shares is a
summary. This summary is not complete and is subject to the complete text of our
memorandum of association (the "memorandum") and articles of association (the
"articles"). Our memorandum and articles are exhibits to the registration
statement and are incorporated herein by reference. We encourage you to read
those documents carefully.

                        DESCRIPTION OF ORDINARY SHARES

VOTING

     The holders of ordinary shares are entitled to one vote per share other
than on the election of directors.

     With respect to the election of directors, each holder of ordinary shares
entitled to vote at the election has the right to vote, in person or by proxy,
the number of shares held by him for as many persons as there are directors to
be elected and for whose election that holder has a right to vote. The directors
are divided into three classes, with only one class being up for election each
year. Directors are elected by a plurality of the votes cast in the election.
Cumulative voting for the election of directors is prohibited by our articles.

     There are no limitations imposed by Cayman Islands law or our articles on
the right of nonresident shareholders to hold or vote their ordinary shares.

     The rights attached to any separate class or series of shares, unless
otherwise provided by the terms of the shares of that class or series, may be
varied only with the consent in writing of the holders of all of the issued
shares of that class or series or by a special resolution passed at a separate
general meeting of holders of the shares of that class or series. The necessary
quorum for that meeting is the presence of holders of at least a majority of the
shares of that class or series. Each holder of shares of the class or series
present, in person or by proxy, has one vote for each share of the class or
series of which he is the holder. Outstanding shares will not be deemed to be
varied by the creation or issuance of further shares that rank in any respect
prior to or equivalent with those shares.

     Under Cayman Islands law, some matters, like altering the memorandum or the
articles, changing our name, voluntarily winding up the company or resolving to
be registered by way of continuation in a jurisdiction outside the Cayman
Islands, require approval of shareholders by a special resolution. A special
resolution is a resolution (1) passed by the holders of two-thirds of the shares
voted at a general meeting or (2) approved in writing by all shareholders
entitled to vote at a general meeting of the company.

                                       14
<PAGE>

QUORUM FOR GENERAL MEETINGS

     The presence of shareholders, in person or by proxy, holding at least a
majority of the issued shares generally entitled to vote at a meeting, is a
quorum for the transaction of most business. However, different quorums are
required in some cases to approve a change in our articles.

     The presence of shareholders, in person or by proxy, holding at least 95%
of the issued shares entitled to vote at a meeting is the required quorum at a
general meeting to consider or adopt a special resolution to amend, vary,
suspend the operation of or cause any of the following provisions of the
articles to cease to apply:

     .   Section 17 -- which relates to the convening of general meetings

     .   Section 19 -- which relates to proceedings and procedures at general
         meetings

     .   Section 21.1 -- which relates to the election and appointment of
         directors

     .   Section 26 -- which generally requires shareholders to approve the
         sale, lease or exchange of all or substantially all of our property or
         assets, or

     .   Section 27 -- which requires shareholders to approve business
         combinations with interested shareholders (with the exceptions
         described below)

     However, the presence of shareholders, in person or by proxy, holding at
least a majority of the issued shares entitled to vote at the meeting is a
quorum if:

     .   a majority of the board of directors has, at or prior to the meeting,
         recommended a vote in favor of the special resolution, and

     .   in the case of a special resolution to amend, vary, suspend the
         operation of or disapply Section 27 of the articles, other than a
         special resolution referred to below, the favorable board of directors'
         recommendation is made at a time when a majority of the board of
         directors then in office were directors prior to any person becoming an
         interested member during the previous three years or were recommended
         for election or elected to succeed those directors by a majority of
         those directors

     In addition, the presence of shareholders, in person or by proxy, holding
at least a majority of the issued shares entitled to vote at a meeting is also
the required quorum to consider or adopt a special resolution to delete Section
27 of the articles if:

     .   the resolution will not be effective until 12 months after the
         passing of the resolution, and

     .   the restriction in Section 27 of the articles will otherwise continue
         to apply to any business combination between us and any person who
         became an interested shareholder on or prior to the passing of the
         resolution

     The shareholders present at a duly constituted general meeting may continue
to transact business until adjournment, despite the withdrawal of shareholders
that leave less than a quorum.

DIVIDEND RIGHTS

     Subject to any rights and restrictions of any other class or series of
shares, the board of directors may, from time to time, declare dividends on the
shares issued and authorize payment of the dividends out of our lawfully
available funds. The board of directors may declare that any dividend be paid
wholly or partly by the distribution of our shares and/or specific assets.

                                       15
<PAGE>


RIGHTS UPON LIQUIDATION

     Upon our liquidation, after the full amounts that holders of any issued
shares ranking senior to the ordinary shares as to distribution on liquidation
or winding up are entitled to receive have been paid or set aside for payment,
the holders of ordinary shares are entitled to receive, pro rata, any remaining
assets available for distribution to the holders of ordinary shares. The
liquidator may deduct from the amount payable in respect of those ordinary
shares any liabilities the holder has to or with us.  The assets received by the
holders of ordinary shares in a liquidation may consist in whole or in part of
property. That property is not required to be of the same kind for all
shareholders.

NO SINKING FUND

     The ordinary shares have no sinking fund provisions.

NO LIABILITY FOR FURTHER CALLS OR ASSESSMENTS

     The ordinary shares that have been issued to date are fully paid and
nonassessable.  Any ordinary shares we offer under this prospectus will be fully
paid and nonassessable.

NO PREEMPTIVE RIGHTS

     Holders of ordinary shares will have no preemptive or preferential right to
purchase any of our securities.

REDEMPTION AND CONVERSION

     The ordinary shares are not convertible into shares of any other class or
series or subject to redemption either by us or the holder of the shares.

REPURCHASE

     Under our articles, we may re-purchase any issued ordinary shares in the
circumstances and on the terms agreed by the holder of the shares, whether or
not we have made a similar offer to any other holders of ordinary shares.

RESTRICTIONS ON TRANSFER

     Subject to the rules of any stock exchange on which the ordinary shares may
be listed, the board of directors may, in its absolute discretion and without
assigning any reason, decline to register any transfer of shares.

COMPULSORY ACQUISITION OF SHARES HELD BY MINORITY HOLDERS

     An acquiring party is generally able to acquire compulsorily the ordinary
shares of minority holders in one of two ways:

     .   By a procedure under the Companies Law of the Cayman Islands known as a
         "scheme of arrangement." A scheme of arrangement is made by obtaining
         the consent of the Cayman Islands corporation, the consent of the court
         and approval of the arrangement by holders of ordinary shares (1)
         representing a majority in number of the shareholders present at the
         meeting held to consider the arrangement and (2) holding at least 75%
         of all the issued ordinary shares other than those held by the
         acquiring party, if any. If a scheme of arrangement receives all
         necessary consents, all holders of ordinary shares of a company would
         be compelled to sell their shares under the terms of the scheme of
         arrangement.

     .   By acquiring pursuant to a tender offer 90% of the ordinary shares not
         already owned by the acquiring party (the "offeror"). If an offeror
         has, within four months after the making of an offer for all the
         ordinary shares not owned by the offeror, obtained the approval of not
         less than 90% of all the shares to which the offer relates, the offeror
         may, at any time within two months after the

                                       16
<PAGE>


         end of that four-month period, require any nontendering shareholder to
         transfer its shares on the same terms as the original offer. In those
         circumstances, nontendering shareholders will be compelled to sell
         their shares, unless within one month from the date on which the notice
         to compulsorily acquire was given to the nontendering shareholder, the
         nontendering shareholder is able to convince the court to order
         otherwise.

STOCK EXCHANGE LISTING

     The ordinary shares are listed on the New York Stock Exchange and trade
under the symbol "RIG."

TRANSFER AGENT

     The transfer agent and registrar for the ordinary shares is The Bank of New
York.

                       DESCRIPTION OF PREFERENCE SHARES

     The board of directors is authorized, without obtaining any vote or consent
of the holders of any class or series of shares unless expressly provided by the
terms of issue of that class or series, to provide from time to time for the
issuance of up to 50,000,000 preference shares in one or more classes or series
of shares.  The board of directors can also establish the characteristics of
each class or series, including the number of shares, designations, relative
voting rights, dividend rights, liquidation and other rights, redemption,
repurchase or exchange rights and any other preferences and relative,
participating, optional or other rights and limitations not inconsistent with
applicable law.

     We have summarized selected provisions of the preference shares in this
section.  This summary is not complete.  If we offer any preference shares, we
will file the form of the preference shares with the SEC, and you should read it
for provisions that may be important to you.

     The prospectus supplement relating to any series of preference shares being
offered will describe that series of preference shares and include specific
terms relating to the offering.  The prospectus supplement will include some or
all of the following:

     .   the title of the preference shares

     .   the maximum number of shares of the series

     .   the dividend rate or the method of calculating the dividend, the date
         from which dividends will accrue and whether dividends will be
         cumulative

     .   procedures for any auctioning or remarketing of the preference shares

     .   any liquidation preference

     .   any optional redemption provisions

     .   any sinking fund or other provisions that would obligate us to redeem
         or purchase the preference shares

     .   any terms for the conversion or exchange of the preference shares for
         our debt securities, ordinary shares or other preference shares

     .   any voting rights

     .   any other preferences and relative, participating, optional or other
         special rights and limitations

                                       17
<PAGE>


     Any preference shares we offer under this prospectus will be fully paid and
nonassessable.  The transfer agent and registrar for each series will be
described in the related prospectus supplement.

                            DESCRIPTION OF WARRANTS

     We may issue warrants to purchase debt securities or preference shares.  We
may issue warrants independently or together with other securities, and warrants
sold with other securities may be attached to or separate from the other
securities.  Warrants will be issued under one or more warrant agreements
between us and a warrant agent that we will name in the prospectus supplement.

     We have summarized selected provisions of the warrants and the warrant
agreements below.  This summary is not complete.  If we offer any warrants, we
will file the form of any warrant certificate and warrant agreement with the
SEC, and you should read the warrant certificate and warrant agreement for
provisions that may be important to you.

     The prospectus supplement relating to any warrants being offered will
describe the warrants and include specific terms relating to the offering.  The
prospectus supplement will include some or all of the following:

     .   the title of the warrants

     .   the aggregate number of warrants offered

     .   the designation, number and terms of the debt securities or preference
         shares purchasable upon exercise of the warrants, and procedures that
         will result in the adjustment of those numbers

     .   the exercise price of the warrants

     .   the dates or periods during which the warrants are exercisable

     .   the designation and terms of any securities with which the warrants
         are issued

     .   if the warrants are issued as a unit with another security, the date on
         and after which the warrants and the other security will be separately
         transferable

     .   if the exercise price is not payable in U.S. dollars, the foreign
         currency, currency unit or composite currency in which the exercise
         price is denominated

     .   any minimum or maximum amount of warrants that may be exercised at any
         one time

     .   any terms, procedures and limitations relating to the transferability,
         exchange or exercise of the warrants

     .   any other terms of the warrants

     Warrant certificates will be exchangeable for new warrant certificates of
different denominations at the office indicated in the prospectus supplement.
Prior to the exercise of their warrants, holders of warrants will not have any
of the rights of holders of the securities subject to the warrants.

MODIFICATIONS

     We may amend the warrant agreements and the warrants, without the consent
of the holders of the warrants, to cure any ambiguity, to cure, correct or
supplement any defective or inconsistent provision, or in any other manner that
will not materially and adversely affect the interests of holders of outstanding
warrants.

                                       18
<PAGE>


ENFORCEABILITY

     The warrant agent will act solely as our agent. The warrant agent will not
have any duty or responsibility if we default under the warrant agreements or
the warrant certificates. A warrant holder may, without the consent of the
warrant agent, enforce by appropriate legal action on its own behalf the
holder's right to exercise the holder's warrants.

                           ANTI-TAKEOVER PROVISIONS

     Our articles include provisions that could have an anti-takeover effect.
These provisions are intended to enhance the likelihood of continuity and
stability in the composition of the board of directors and in the policies
formulated by the board of directors, and may have the effect of discouraging
actual or threatened changes of control.

     The articles provide that our board of directors will be divided into three
classes serving staggered three-year terms. Directors can be removed from office
only for cause, as defined in the articles, by the affirmative vote of the
holders of a majority of the issued shares generally entitled to vote.  The
board of directors does not have the power to remove directors. Vacancies on the
board of directors may be filled only by the remaining directors and not by the
shareholders. Each of these provisions can delay a shareholder from obtaining
majority representation on the board of directors.

     The articles provide that the board of directors will consist of at least
two and not more than twelve persons, the exact number to be set from time to
time by a majority of the whole board of directors. Accordingly, the board of
directors, and not the shareholders, has the authority to determine the number
of directors and could delay any shareholder from obtaining majority
representation on the board of directors by enlarging the board of directors and
filling the new vacancies with its own nominees until a general meeting at which
directors are to be appointed.

     The articles establish an advance notice procedure that must be followed by
shareholders if they wish to nominate candidates for election as directors or
propose any business at an annual general meeting of shareholders. The articles
provide generally that, if a shareholder desires to propose any business at an
annual general meeting, that shareholder must give us notice not less than 90
days prior to the anniversary of the originally scheduled date of the
immediately preceding annual general meeting. However, if the date of the
forthcoming annual general meeting is more than 30 days before or after the
anniversary date, the deadline is the close of business on the tenth day after
we publicly disclose the meeting date. In each case, the notice must contain
specified information concerning the shareholder submitting the proposal.

     Subject to the terms of any other class of shares in issue, any action
required or permitted to be taken by the holders of ordinary shares must be
taken at a duly called annual or special general meeting of shareholders unless
taken by written consent of all holders of ordinary shares. Special general
meetings may be called only by a majority of the entire board of directors.

     The board of directors is authorized, without obtaining any vote or consent
of the holders of any class or series of shares unless expressly provided by the
terms of issue of a class or series, to issue from time to time any other
classes or series of shares with the designations and relative powers,
preferences, conversion or other rights, voting powers, restrictions,
limitations as to dividends or terms or conditions of redemption as it considers
fit. The board of directors could authorize the issuance of preference shares
with terms and conditions that could discourage a takeover or other transaction
that holders of some or a majority of the ordinary shares might believe to be in
their best interests or in which holders might receive a premium for their
shares over the then market price of the shares. No preference shares have been
established as of the date of this prospectus.

     The special quorum provisions contained in the articles require the holders
of 95% of all the voting shares to be present, in person or by proxy, at a
general meeting to consider or adopt a special resolution to amend, vary,
suspend the operation of or cease the application of the following provisions of
the articles, unless a majority of the board of directors has recommended that
the shareholders vote in favor of the special resolution:

                                       19
<PAGE>


     .   Section 17 -- which relates to the convening of general meetings

     .   Section 19 -- which relates to proceedings and procedures at general
         meetings

     .   Section 21.1 -- which relates to the election and appointment of
         directors

     .   Section 26 -- which generally requires shareholders to approve the
         sale, lease or exchange of all or substantially all of our property or
         assets, or

     .   Section 27 -- which requires shareholders to approve business
         combinations with interested members

     For a description of exceptions to the quorum requirements to amend Section
27, see the discussion under the heading "Description of Ordinary Shares --
Quorum for General Meetings."

     As a Cayman-incorporated company, we are not subject to Section 203 of the
Delaware General Corporation Law, which restricts business combinations with
interested shareholders.  However, the articles contain provisions that largely
mirror the intention of Section 203 and generally prohibit "business
combinations" between us and an "interested shareholder."  Specifically,
"business combinations" between us and an interested member are prohibited for a
period of three years after the time the interested member acquired its shares,
unless:

     .   the business combination or the transaction resulting in the person
         becoming an interested member is approved by the board of directors
         prior to the date the interested member acquired shares

     .   the interested member acquired at least 85% of our shares in the
         transaction in which it became an interested member, or

     .   the business combination is approved by a majority of the board of
         directors and by the affirmative vote of disinterested shareholders
         holding at least two-thirds of the shares generally entitled to vote

     "Business combinations" is defined broadly to include mergers,
consolidations of majority owned subsidiaries, sales or other dispositions of
assets having an aggregate value in excess of 10% of our consolidated assets,
and most transactions that would increase the interested shareholder's
proportionate share ownership.

     "Interested member" is defined as a person who, together with any
affiliates and/or associates of that person, beneficially owns, directly or
indirectly, 15% or more of our issued voting shares.

                             PLAN OF DISTRIBUTION

     We may sell the offered securities in and outside the United States (1)
through underwriters or dealers, (2) directly to purchasers or (3) through
agents.  The prospectus supplement will set forth the following information:

     .   the terms of the offering
     .   the names of any underwriters or agents
     .   the purchase price
     .   the net proceeds to us
     .   any delayed delivery arrangements
     .   any underwriting discounts and other items constituting underwriters'
         compensation
     .   any initial public offering price
     .   any discounts or concessions allowed or reallowed or paid to dealers

SALE THROUGH UNDERWRITERS OR DEALERS

     If we use underwriters in the sale, the underwriters will acquire the
securities for their own account.  The underwriters may resell the securities
from time to time in one or more transactions, including negotiated

                                       20
<PAGE>


transactions, at a fixed public offering price or at varying prices determined
at the time of sale.  Underwriters may offer securities to the public either
through underwriting syndicates represented by one or more managing underwriters
or directly by one or more firms acting as underwriters.  Unless we inform you
otherwise in the prospectus supplement, the obligations of the underwriters to
purchase the securities will be subject to certain conditions, and the
underwriters will be obligated to purchase all the offered securities if they
purchase any of them.  The underwriters may change from time to time any initial
public offering price and any discounts or concessions allowed or reallowed or
paid to dealers.

     During and after an offering through underwriters, the underwriters may
purchase and sell the securities in the open market.  These transactions may
include overallotment and stabilizing transactions and purchases to cover
syndicate short positions created in connection with the offering.  The
underwriters may also impose a penalty bid, in which selling concessions allowed
to syndicate members or other broker-dealers for the offered securities sold for
their account may be reclaimed by the syndicate if such offered securities are
repurchased by the syndicate in stabilizing or covering transactions.  These
activities may stabilize, maintain or otherwise affect the market price of the
offered securities, which may be higher than the price that might otherwise
prevail in the open market.  If commenced, these activities may be discontinued
at any time.

     If we use dealers in the sale of securities, we will sell the securities to
them as principals.  They may then resell those securities to the public at
varying prices determined by the dealers at the time of resale.  We will include
in the prospectus supplement the names of the dealers and the terms of the
transaction.

DIRECT SALES AND SALES THROUGH AGENTS

     We may sell the securities directly.  In that event, no underwriters or
agents would be involved.  We may also sell the securities through agents we
designate from time to time.  In the prospectus supplement, we will name any
agent involved in the offer or sale of the offered securities, and we will
describe any commissions payable by us to the agent.  Unless we inform you
otherwise in the prospectus supplement, any agent will agree to use its
reasonable best efforts to solicit purchases for the period of its appointment.

     We may sell the securities directly to institutional investors or others
who may be deemed to be underwriters within the meaning of the Securities Act of
1933 with respect to any sale of those securities.  We will describe the terms
of any such sales in the prospectus supplement.

DELAYED DELIVERY CONTRACTS

     If we so indicate in the prospectus supplement, we may authorize agents,
underwriters or dealers to solicit offers from certain types of institutions to
purchase securities from us at the public offering price under delayed delivery
contracts.  These contracts would provide for payment and delivery on a
specified date in the future.  The contracts would be subject only to those
conditions described in the prospectus supplement.  The prospectus supplement
will describe the commission payable for solicitation of those contracts.

GENERAL INFORMATION

     We may have agreements with the agents, dealers and underwriters to
indemnify them against certain civil liabilities, including liabilities under
the Securities Act of 1933, or to contribute with respect to payments that the
agents, dealers or underwriters may be required to make.  Agents, dealers and
underwriters may be our customers, may engage in transactions with us, or may
perform services for us in the ordinary course of their businesses.

     The securities may or may not be listed on a national securities exchange.
We cannot assure you that there will be a market for the securities.

                                LEGAL OPINIONS

     The validity of the debt securities and warrants offered hereby has been
passed upon by Eric B. Brown, Esq., our Vice President, General Counsel and
Secretary.  As of June 1, 1999, Mr. Brown owned directly or

                                       21
<PAGE>


indirectly approximately 10,000 ordinary shares and owned directly options to
purchase 43,034 ordinary shares. The validity of the ordinary shares and
preference shares offered hereby has been passed upon by our Cayman Islands
counsel, W.S. Walker & Company, Cayman Islands. Any underwriters will be advised
about issues relating to any offering by their own legal counsel.

                                    EXPERTS

     Ernst & Young LLP, independent auditors, have audited the consolidated
financial statements included in Transocean-Delaware's Annual Report on Form 10-
K for the year ended December 31, 1998, as set forth in their report, which is
incorporated by reference in this prospectus.  Transocean-Delaware's financial
statements are incorporated by reference in reliance on Ernst & Young LLP's
report, given on their authority as experts in accounting and auditing.

                                       22
<PAGE>


                                    PART II

                    INFORMATION NOT REQUIRED IN PROSPECTUS

ITEM 14. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION.

     The following table sets forth the estimated expenses payable by the
Company in connection with the offering described in this Registration
Statement.

                Registration Fee...............   $132,750
                Printing expenses..............    100,000
                Accounting fees and expenses...    100,000
                Legal fees and expenses........    133,000
                Blue Sky fees and expenses.....     20,000
                Trustee fees and expenses......     20,000
                Rating agency fees.............    200,000
                Miscellaneous..................     94,250
                   Total.......................   $800,000
                                                  ========

ITEM 15. INDEMNIFICATION OF DIRECTORS AND OFFICERS.

     Section 34.1 of the Company's Articles of Association provides that:

     No directors will be personally liable to the Company or, if any, its
     members for monetary damages for breach of fiduciary duty as a director,
     except for liability (i) for any breach of the director's duty of loyalty
     to the Company or, if any, to its members, (ii) for acts or omissions not
     in good faith or that involve intentional misconduct or a knowing violation
     of law or (iii) for any transaction from which the director derived an
     improper personal benefit.

     The Company will indemnify, to the fullest extent permitted by the laws of
     the Cayman Islands as from time to time in effect, if any, any person who
     was or is a party or is threatened to be made a party to, or otherwise
     requires representation by counsel in connection with, any threatened,
     pending or completed action, suit or proceeding, whether civil, criminal,
     administrative or investigative (whether or not an action by or in the
     right of the Company) by reason of the fact that he is or was a director or
     officer of the Company, or, while serving as a director or officer of the
     Company, 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.  The right to indemnification
     conferred by Section 34.1 also includes the right of such persons to be
     paid in advance by the Company for their expenses to the fullest extent
     permitted by the laws of the Cayman Islands as from time to time in effect.

     Unless otherwise determined by the Company's  board of directors, the
     Company will indemnify to the fullest extent permitted by the laws of the
     Cayman Islands as from time to time in effect, if any, any person who was
     or is a party or is threatened to be made a party to, or otherwise requires
     representation by counsel in connection with, any threatened, pending or
     completed action, suit or proceeding, whether civil, criminal,
     administrative or investigative (whether or not an action by or in the
     right of the Company), by reason of the fact that he is or was an employee
     (other than an officer) or agent 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.

     The rights and authority conferred by Section 34.1 are not exclusive of any
     other right that any person has or hereafter acquires under any law,
     provision of the Company's Articles of Association or Memorandum of
     Association, agreement, vote of members of the Company or of the board of
     directors of the Company or otherwise.

                                      II-1
<PAGE>


     The Company also has directors and officers liability insurance that would
indemnify its directors and officers 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.

     Agreements that may be entered into with underwriters, dealers and agents
who participate in the distribution of securities of the Company may contain
provisions relating to the indemnification of the Company's officers and
directors.

ITEM 16.  EXHIBITS.*

EXHIBIT NO.  DESCRIPTION OF EXHIBIT
- -----------  ----------------------
  *1         Form of Underwriting Agreement

  +4.1       Memorandum of Association of the Company (incorporated by
             reference to Annex B to the proxy statement/prospectus included in
             Transocean-Texas's Registration Statement on Form S-4
             (Registration No. 333-75899) dated April 8, 1999)

  +4.2       Articles of Association of the Company (incorporated by reference
             to Annex C to the proxy statement/prospectus included in
             Transocean-Texas's Registration Statement on Form S-4
             (Registration No. 333-75899) dated April 8, 1999)

  +4.3       Senior Indenture dated as of April 15, 1997 between Transocean-
             Delaware and Chase Bank of Texas, National Association, as trustee
             (incorporated by reference to Exhibit 4.1 to Transocean-Delaware's
             Current Report on Form 8-K dated April 29, 1997)

  +4.4       First Supplemental Indenture dated as of April 15, 1997 between
             Transocean-Delaware and Chase Bank of Texas, National Association,
             as trustee (incorporated by reference to Exhibit 4.2 to Transocean-
             Delaware's Current Report on Form 8-K dated April 29, 1997)

  4.5        Second Supplemental Indenture dated as of May 14, 1999 between the
             Company and Chase Bank of Texas, National Association, as trustee

  +4.6       Form of Subordinated Indenture (incorporated by reference to
             Exhibit 4.3 to Transocean-Delaware's Registration Statement on Form
             S-3 (Registration No. 333-59001)

  5.1        Opinion of Eric B. Brown, Esq.

  5.2        Opinion of W.S. Walker & Company

  12         Statement as computation of ratio of earnings to fixed charges

  23.1       Consent of Ernst & Young LLP

  23.2       Consent of Eric B. Brown, Esq. (included in Exhibit 5.1)

  23.3       Consent of W.S. Walker & Company (included in Exhibit 5.2)

  24         Powers of Attorney

++25.1       Statement of Eligibility and Qualification under the Trust
             Indenture Act of 1939 of Chase Bank of Texas, National Association,
             as trustee

                                      II-2
<PAGE>


             _______________

             +    Incorporated by reference as indicated.

             ++   Previously filed.

             *    The Company will file as an exhibit to a Current Report on
                  Form 8-K (i) any underwriting agreement relating to securities
                  offered hereby, (ii) the instruments setting forth the terms
                  of any debt securities, preference shares or warrants, (iii)
                  any required opinion of counsel as to certain tax matters
                  relative to securities offered hereby or (iv) any Statement of
                  Eligibility and Qualification under the Trust Indenture Act of
                  1939 as to the applicable trustee.

ITEM 17. UNDERTAKINGS.

         (a) The undersigned registrant hereby undertakes:

             (1) To file, during any period in which offers or sales are being
         made, a further 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 this 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;

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

         provided, however, that the undertakings set forth in paragraphs
         (a)(1)(i) and (a)(1)(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 registrant 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.

         (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 that is incorporated by reference in this 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 may be permitted to directors, officers and controlling
     persons of the registrant pursuant to the provisions described under Item
     15 above, 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

                                      II-3
<PAGE>


     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.

         (d) With respect to the Subordinated Indenture referred to in Exhibit
     4.6 to this Registration Statement, the undersigned registrant hereby
     undertakes to file an application for the purpose of determining the
     eligibility of the trustee to act under subsection (a) of section 310 of
     the Trustee Indenture Act (the "TIA") in accordance with the rules and
     regulations prescribed by the Commission under section 305(b)(2) of
     the TIA.

                                      II-4
<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-3 and has duly caused this Post-Effective
Amendment to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, the State of Texas, on June 28, 1999.


                                     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 POST-
EFFECTIVE AMENDMENT HAS BEEN SIGNED BY THE FOLLOWING PERSONS IN THE CAPACITIES
INDICATED ON JUNE 28, 1999.

              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 (Principal
        Robert L. Long                   Financial Officer)


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

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

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

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

                 *                       Director
- -----------------------------------
        Robert J. Lanigan

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

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

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

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


* By: /s/ Nicolas J. Evanoff
      -----------------------------
           Nicolas J. Evanoff
            Attorney in Fact

                                      II-5

<PAGE>

                                                                     EXHIBIT 4.5
================================================================================

                       TRANSOCEAN OFFSHORE (TEXAS) INC.,

                           TRANSOCEAN OFFSHORE INC.

                                      AND

                           CHASE BANK OF TEXAS, N.A.

                                    TRUSTEE

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

                         SECOND SUPPLEMENTAL INDENTURE

                                  DATED AS OF

                                 MAY 14, 1999


                                      TO

                                   INDENTURE

                                  DATED AS OF

                                APRIL 15, 1997


================================================================================
<PAGE>

          SECOND SUPPLEMENTAL INDENTURE, dated as of May 14, 1999, between
TRANSOCEAN OFFSHORE (TEXAS) INC., a corporation duly organized and existing
under the laws of the State of Texas (herein called the "Transocean-Texas"),
TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company limited by shares
("Transocean-Cayman"), each having its principal office at 4 Greenway Plaza,
Houston, Texas 77046, and CHASE BANK OF TEXAS, N.A. (formerly, Texas Commerce
Bank National Association), as Trustee (herein called the "Trustee"), the office
of the Trustee at which at the date hereof its corporate trust business is
principally administered being 600 Travis Street, Suite 1150, Houston, Texas
77002.

                            RECITALS OF THE COMPANY

          Transocean Offshore Inc., a Delaware corporation (the "Company"), has
executed and delivered to the Trustee an Indenture, dated as of April 15, 1997
(the "Original Indenture" and as supplemented by a First Supplemental Indenture,
dated as of April 15, 1997, and by this Second Supplemental Indenture, the
"Indenture"), providing for the issuance from time to time of the Company's
unsecured debentures, notes or other evidences of indebtedness (herein called
the "Securities"), issuable in one or more series as in the Indenture provided.
All capitalized terms used herein which are defined in the Original Indenture
shall have the meanings assigned thereto in the Original Indenture unless
otherwise defined herein.

          Pursuant to an Agreement and Plan of Merger and Conversion dated as of
March 12, 1999 between the Company and Transocean-Texas, the Company will be
merged (the "Merger") with and into Transocean-Texas, with Transocean-Texas to
be the surviving corporation, and following such Merger, Transocean-Texas will
convert to and register by way of continuation and continue its existence as
(the "Conversion") Transocean -Cayman.

          Section 801(1) of the Original Indenture provides that Transocean-
Texas, as the surviving corporation of the Merger, is required to expressly
assume, by an indenture supplemental to the Original Indenture, the due and
punctual payment of the principal of (and premium, if any) and interest
(including Additional Amounts, if any) on all the Securities and the performance
of every covenant of the Original Indenture on the part of the Company to be
performed or observed.

          Section 801(1) of the Original Indenture may be deemed to provide that
Transocean-Cayman, as a result of the Conversion, is required to expressly
assume, by an indenture supplemental to the Original Indenture, the due and
punctual payment of the principal of (and premium, if any) and interest
(including Additional Amounts, if any) on all the Securities and the performance
of every covenant of the Original Indenture on the part of the Company to be
performed or observed.

          Section 901(1) of the Original Indenture permits the execution of
supplemental indentures without the consent of any Holders to evidence the
succession of another Person to the Company and the assumption by any such
successor of the covenants of the Company in the Original Indenture and in the
Securities.
<PAGE>

          Pursuant to the foregoing authority, Transocean-Texas and Transocean-
Cayman propose in and by this Second Supplemental Indenture to supplement and
amend the Original Indenture.

          All things necessary to make this Second Supplemental Indenture a
valid agreement of Transocean-Texas and Transocean-Cayman, in accordance with
its terms, have been done.

          NOW, THEREFORE, THIS SECOND SUPPLEMENTAL INDENTURE WITNESSETH:

          For and in consideration of the premises and the purchase of the
Securities by the Holders thereof, it is mutually covenanted and agreed, for the
equal and proportionate benefit of all Holders of the Securities or of series
thereof, as follows:

     Section 1.  Succession by Merger.  As of the effective time of the Merger,
Transocean-Texas shall become the successor to the Company for all purposes of
the Indenture and Transocean-Texas hereby expressly assumes the due and punctual
payment of the principal of (and premium, if any) and interest (including
Additional Amounts, if any) on all the Securities and the performance of every
covenant of the Indenture, as supplemented by this Second Supplemental
Indenture, on the part of the Company to be performed or observed.

     Section 2.  Succession by Conversion.  As of the effective time of the
Conversion, Transocean-Cayman shall become the successor to Transocean-Texas for
all purposes of the Indenture and Transocean-Cayman hereby expressly assumes the
due and punctual payment of the principal of (and premium, if any) and interest
(including Additional Amounts, if any) on all the Securities and the performance
of every covenant of the Indenture, as supplemented by this Second Supplemental
Indenture, on the part of Transocean-Texas to be performed or observed.

     Section 3.  Ratification.  The Indenture, as hereby supplemented, is in all
respects ratified and confirmed by each of the parties hereto, and all of the
rights and powers created thereby or thereunder shall be and remain in full
force and effect.


                                   *   *   *

          This instrument may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but all such counterparts
shall together constitute but one and the same instrument.

                                      -2-
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Second
Supplemental Indenture to be duly executed, and their respective corporate seals
to be hereunto affixed and attested, all as of the day and year first above
written.

                                   TRANSOCEAN OFFSHORE (TEXAS) INC.,
                                   a Texas corporation


[CORPORATE SEAL]                   By  /s/ Nicolas J. Evanoff
                                       ----------------------------------
                                         Name:  Nicolas J. Evanoff
                                         Title: Attorney in Fact



                                   TRANSOCEAN OFFSHORE INC., a
                                   Cayman Islands exempted company limited by
                                   shares


[CORPORATE SEAL]                   By  /s/ Eric B. Brown
                                       ----------------------------------
                                         Name:  Eric B. Brown
                                         Title: Vice President



                                   CHASE BANK OF TEXAS, N.A., Trustee


[CORPORATE SEAL]                   By  /s/ Mauri J. Cowan
                                       ----------------------------------
                                         Name:  Mauri J. Cowan
                                         Title: Vice President and Trust Officer

                                      -3-
<PAGE>

STATE OF TEXAS      (S)
                    (S)  ss.
COUNTY OF HARRIS    (S)


          This instrument was acknowledged before me on the 14th day of May,
1999, by Nicolas Evanoff, as Attorney-in-Fact of TRANSOCEAN OFFSHORE (TEXAS)
INC., a Texas corporation.



                                       /s/ Donna Leah Goode
                                       ----------------------------------
                                       Notary Public

[NOTARIAL SEAL]



STATE OF TEXAS      (S)
                    (S)  ss:
COUNTY OF HARRIS    (S)


          This instrument was acknowledged before me on the 14th day of May,
1999, by Eric B. Brown, as Vice President of TRANSOCEAN OFFSHORE INC., a Cayman
Islands exempted company limited by shares.



                                       /s/ Donna Leah Goode
                                       ----------------------------------
                                       Notary Public

[NOTARIAL SEAL]

                                      -4-
<PAGE>

STATE OF TEXAS      (S)
                    (S)  ss:
COUNTY OF HARRIS    (S)


          This instrument was acknowledged before me on the 14th day of May,
1999, by Mauri Cowan, as Vice President and Trust Officer of CHASE BANK OF
TEXAS, N.A.



                                       /s/ Delores B. Lynch
                                       ----------------------------------
                                       Notary Public

[NOTARIAL SEAL]

                                      -5-

<PAGE>

                                                                     EXHIBIT 5.1

June 23, 1999


Transocean Offshore Inc.
4 Greenway Plaza
Houston, Texas 77046

Gentlemen:

As set forth in Post-Effective Amendment No.1 (the "Amendment") to Registration
Statement on Form S-3 (Registration No. 333-24457) to be filed with the
Securities and Exchange Commission (the "Commission") on June 23, 1999 (the
"Registration Statement") by Transocean Offshore Inc., a Cayman Islands exempted
company (the "Company"), under the Securities Act of 1993, as amended (the
"Act"), relating to (i) unsecured debt securities (the "Debt Securities"), in
one or more series, which may be convertible into or exchangeable for the
Company's ordinary shares, par value $0.01 per share (the "Ordinary Shares"),
the Company's preference shares, par value $0.10 per share (the "Preference
Shares"), or other Debt Securities; (ii) Preference Shares, in one or more
series, which may be convertible into or exchangeable for Ordinary Shares, Debt
Securities or other Preference Shares; (iii) warrants to purchase Debt
Securities or Preference Shares (the "Warrants"); and (iv) Ordinary Shares to be
issued and sold by the Company from time to time pursuant to Rule 415 under the
Act for an aggregate initial offering price not to exceed $450,000,000, certain
legal matters in connection with such Debt Securities and Warrants
(collectively, the "Securities") are being passed upon by me.

I am Vice President and General Counsel of the Company.  In such capacity, I
have examined (i) the Articles of Association and Memorandum of Association of
the Company (the "Charter Documents"); (ii)  the Indenture dated as of April 15,
1997, as supplemented by the First Supplemental Indenture dated as of April 15,
1997 and the Second Supplemental Indenture dated as of May 14, 1999 (the "Senior
Indenture"), between the Company and Chase Bank of Texas, National Association,
as trustee, pursuant to which the senior Debt Securities may be issued; (iii)
the Indenture (the "Subordinated Indenture" and, together with the Senior
Indenture, the "Indentures") in the form of Exhibit 4.6 to the Registration
Statement to be executed by the Company and a trustee to be designated therein,
pursuant to which subordinated Debt Securities may be issued; and (iv) the
originals, or copies certified or otherwise identified, of corporate records of
the Company, certificates of public officials and of representatives of the
Company, statutes and other instruments and documents as a basis for the
opinions hereafter expressed.

In connection with this opinion, I have assumed that (i) the Amendment and any
further amendments to the Registration Statement (including post-effective
amendments), will have become effective; (ii) a prospectus supplement will have
been prepared and filed with the Commission describing the
<PAGE>

Securities offered thereby; (iii) all Securities will be issued and sold in
compliance with applicable federal and state securities laws and in the manner
stated in the Registration Statement and the appropriate prospectus supplement;
and (iv) a definitive purchase, underwriting or similar agreement with respect
to any Securities offered, and a warrant agreement with respect to any Warrants
offered, will have been duly authorized and validly executed and delivered by
the Company and the other parties thereto.

Based upon and subject to the foregoing, I am of the opinion that:

1.   With respect to Debt Securities to be issued under the Indentures, when (i)
     the applicable Indenture has been duly qualified under the Trust Indenture
     Act of 1939, as amended; (ii) the Board of Directors of the Company or, to
     the extent permitted by the laws of the Cayman Islands, a duly constituted
     and acting committee thereof (such Board of Directors or committee being
     hereinafter referred to as the "Board"), has taken all necessary corporate
     action to approve the issuance and terms of such Debt Securities, the terms
     of the offering thereof and related matters; and (iii) such Debt Securities
     have been duly executed, authenticated, issued and delivered in accordance
     with the provisions of the applicable Indenture and the applicable
     definitive purchase, underwriting or similar agreement approved by the
     Board (a) upon payment of the consideration therefor provided for therein,
     or (b) in the case of Debt Securities issuable upon conversion or exchange
     of Debt Securities or Preference Shares which, by their respective terms,
     are convertible into or exchangeable for Debt Securities or upon exercise
     of Warrants to purchase Debt Securities, in each case as contemplated by
     the applicable Indenture and the applicable definitive warrant, purchase,
     underwriting or similar agreement approved by the Board upon payment of any
     additional consideration that is payable upon such conversion, exchange or
     exercise, such Debt Securities will be legally issued and will constitute
     valid and binding obligations of the Company, enforceable against the
     Company in accordance with their terms, except as such enforcement is
     subject to (i) any applicable bankruptcy, insolvency, reorganization or
     other law relating to or affecting creditors' rights generally and (ii)
     general principles of equity (regardless of whether such enforceability is
     considered in a proceeding in equity or at law).

2.   With respect to Warrants, when (i) the Board has taken all necessary
     corporate action to approve the issuance of and the terms of the offering
     of the Warrants and related matters; (ii) a warrant agreement shall have
     been duly authorized, executed and delivered by the Company and the
     financial institution designated as warrant agent thereunder; and (iii) the
     certificates representing the Warrants have been duly executed,
     countersigned, registered and delivered in accordance with the applicable
     definitive warrant, purchase, underwriting or similar agreement approved by
     the Board upon payment of the consideration therefor, the Warrants will be
     duly authorized and validly issued.

This opinion is limited to the applicable laws of the State of New York and the
applicable federal laws of the United States.

I hereby consent to the filing of this opinion of counsel as Exhibit 5 to the
Amendment.  I also consent to the reference to me under the heading "Legal
Opinions" in the prospectus forming a part

                                       2
<PAGE>

of the Registration Statement.  In giving this consent, I do not thereby admit
that I am in the category of persons whose consent is required under Section 7
of the Act.

                                Very truly yours,



                                /s/ Eric B. Brown

                                       3

<PAGE>

                                                                     EXHIBIT 5.2

                            W. S. WALKER & COMPANY
                               ATTORNEYS-AT-LAW

                         P.O. Box 265GT, Walker House,
                         Grand Cayman, Cayman Islands
                 Tel:  (345) 949-0100     Fax:  (345) 949-7886
                            Email:  [email protected]



TRANSOCEAN OFFSHORE INC.
(A CAYMAN ISLANDS EXEMPTED COMPANY)
4 GREENWAY PLAZA
HOUSTON, TEXAS 77046
UNITED STATES OF AMERICA

                                                                    23 June 1999

Gentlemen,

VALIDITY OF ISSUE OF ORDINARY SHARES AND PREFERENCE SHARES OF TRANSOCEAN
OFFSHORE INC., A CAYMAN ISLANDS EXEMPTED COMPANY.

As set forth in Post-Effective Amendment No.1 (the "Amendment") to Registration
Statement on Form S-3 (Registration No. 333-24457) to be filed with the
Securities and Exchange Commission (the "Commission") on June 23, 1999 (the
"Registration Statement") by Transocean Offshore Inc., a Cayman Islands exempted
company (the "Company"), under the Securities Act of 1993, as amended (the
"Act"), relating to (i) unsecured debt securities (the "Debt Securities"), in
one or more series, which may be convertible into or exchangeable for the
Company's ordinary shares, nominal or par value $0.01 per share (the "Ordinary
Shares"), the Company's preference shares, nominal or par value $0.10 per share
(the "Preference Shares"), or other Debt Securities; (ii) Preference Shares, in
one or more series, which may be convertible into or exchangeable for Ordinary
Shares, Debt Securities or other Preference Shares; (iii) warrants to purchase
Debt Securities or Preference Shares (the "Warrants"); and (iv) Ordinary Shares
to be issued and sold by the Company from time to time pursuant to Rule 415
under the Act for an aggregate initial offering price not to exceed
$450,000,000, certain legal matters in connection with such Ordinary Shares and
Preference Shares (collectively, the "Securities") are being passed upon by us.

For the purposes of giving this opinion, we have examined the documents listed
in Schedule 1.

In giving this opinion we have relied upon the assumptions set out in Schedule 2
hereto, which we have not independently verified.
<PAGE>

We are Attorneys-at-Law in the Cayman Islands and express no opinion as to any
laws other than the laws of the Cayman Islands in force and as interpreted at
the date hereof.

Based upon the foregoing examinations and assumptions and upon such searches as
we have conducted and having regard to legal considerations which we deem
relevant, we are of the opinion that under the laws of the Cayman Islands:

1.   The Company is a corporation duly organized and validly existing in good
     standing under the laws of the Cayman Islands.

2.   With respect to Ordinary Shares, when (i) the Board of Directors of the
     Company or, to the extent permitted by the laws of the Cayman Islands, a
     duly constituted and acting committee thereof (such Board of Directors or
     committee being hereinafter referred to as the "Board"), has taken all
     necessary corporate action to approve the issuance of and the terms of the
     offering of the Ordinary Shares and related matters; and (ii) certificates
     representing the Ordinary Shares have been duly executed, countersigned,
     registered and delivered in accordance with the applicable definitive
     purchase, underwriting or similar agreement approved by the Board (a) upon
     payment of the consideration therefor (not less than the nominal or par
     value of the Ordinary Shares) provided for therein, or (b) in the case of
     Ordinary Shares issuable upon conversion or exchange of Debt Securities or
     Preference Shares which, by their respective terms, are convertible into or
     exchangeable for Ordinary Shares, as contemplated by the applicable
     definitive purchase, underwriting or similar agreement, upon payment of any
     additional consideration that is payable upon such conversion or exchange
     or exercise, the Ordinary Shares will be duly authorized, validly issued,
     fully paid and non-assessable.

3.   With respect to Preference Shares, when (i) the Board has taken all
     necessary corporate action to approve the issuance of and the terms of the
     offering of the Preference Shares and related matters; (ii) a series of
     Preference Shares has been duly authorized and established in accordance
     with the Company's Charter Documents and applicable law; and (iii)
     certificates representing the Preference Shares have been duly executed,
     countersigned, registered and delivered in accordance with the applicable
     definitive warrant, purchase, underwriting or similar agreement approved by
     the Board (a) upon payment of the consideration therefor (not less than the
     nominal or par value of the Preference Shares) provided for therein, or (b)
     in the case of Preference Shares issuable upon conversion or exchange of
     Debt Securities or Preference Shares which, by their respective terms, are
     convertible into or exchangeable for Ordinary Shares, or upon exercise of
     Warrants to purchase Preference Shares, in each case as contemplated by the
     applicable definitive warrant, purchase, underwriting or similar agreement,
     upon payment of any additional consideration that is payable upon such
     conversion, exchange or exercise, the Preference Shares will be duly
     authorized, validly issued, fully paid and non-assessable.

This opinion is limited to the matters referred to herein and shall not be
construed as extending to any other matter or document not referred to herein.
This opinion is given solely for your benefit

                                       2
<PAGE>

and may not be relied upon by any other person without our prior written
consent. This opinion is governed by and shall be construed in accordance with
the laws of the Cayman Islands.

We hereby consent to the filing of this opinion as an exhibit to the Amendment.
We also consent to the reference to us under the heading "Legal Opinions" in the
prospectus forming a part of the Registration Statement. In giving this consent
we do not admit that we are in the category of persons whose consent is required
under Section 7 of the Act.

                                Yours faithfully,

                                /s/ W. S. Walker & Company
                                W. S. WALKER & COMPANY

                                       3
<PAGE>

                                  SCHEDULE 1

                          LIST OF DOCUMENTS EXAMINED


1.   The Memorandum and Articles of Association of the Company in the form they
     became effective upon registration of the Company by way of continuation in
     the Cayman Islands.

2.   The Amendment.

3.   Such other documents as we have considered necessary for the purposes of
     rendering this opinion.
<PAGE>

                                  SCHEDULE 2

                                  ASSUMPTIONS

The opinions hereinbefore given are based upon the following assumptions insofar
as each such assumption may relate to the opinions given:

1.   All original documents are authentic, that all signatures and seals are
     genuine, that all documents purporting to be sealed have been so sealed and
     that all copies conform to their originals.

2.   The Minute Book of the Company supplied to us on June 17, 1999 by the
     Company contain a complete record of the business transacted by it.

3.   The corporate records of the Company supplied to us on June 17, 1999 by the
     Company constitute its complete corporate records and that all matters
     required by law to be recorded therein are so recorded.

4.   The Amendment and any further amendments to the Registration Statement
     (including post-effective amendments) will have become effective.

5.   A prospectus supplement will have been prepared and filed with the
     Commission describing the Securities offered thereby.

6.   All Securities will be issued and sold in compliance with applicable
     federal and state securities laws and in the manner stated in the
     Registration Statement and the appropriate prospectus supplement.

7.   A definitive purchase, underwriting or similar agreement with respect to
     any Securities offered will have been duly authorized and validly executed
     and delivered by the Company and the other parties thereto.

8.   With respect to Ordinary Shares or Preference Shares offered, there will be
     sufficient Ordinary Shares or Preference Shares authorized for issuance by
     the Board of Directors of the Company under the Company's Charter
     Documents.

<PAGE>

                                                                      EXHIBIT 12


                           TRANSOCEAN OFFSHORE INC.

               COMPUTATION OF RATIO OF EARNINGS TO FIXED CHARGES
                     (IN THOUSANDS, EXCEPT RATIO AMOUNTS)
<TABLE>
<CAPTION>
                                      Quarter Ended
                                        March 31,                     Year Ended December 31,
                                     --------------       ----------------------------------------------
                                     1999      1998       1998       1997       1996      1995      1994
                                     ----      ----       ----       ----       ----      ----      ----
<S>                               <C>       <C>        <C>        <C>        <C>        <C>       <C>
Earnings:
     Income before                 $120,895  $110,014   $487,146   $207,245   $121,652   $75,149   $20,239
     income taxes.............
Less:
     Undistributed equity
       in earnings
       (losses) of joint
       ventures...............        3,224     2,366     11,677     10,431      5,659     1,839      (339)

     Interest capitalized
       during the period......        9,744     6,643     33,481     18,165      3,482        --        --

Add:
     Distributed earnings of
       less-than-fifty-percent
       owned joint venture....           --     3,338      3,421         --      3,563        --        --

   Interest expense...........       12,132    13,750     57,373     41,018     10,702     2,519     2,027

     Interest component of
       rental expense.........          668       638      2,674      2,552        764       612       789
                                   --------  --------   --------   --------   --------   -------   -------
       Earnings as adjusted...     $120,727  $118,731   $505,456   $222,219   $127,540   $76,441   $23,394
                                   ========  ========   ========   ========   ========   =======   =======
Fixed Charges:
     Interest costs, including
       capitalized interest...     $ 12,132  $ 13,750   $ 57,373   $ 41,018   $ 10,702   $ 2,519   $ 2,027

     Interest component of
       rental expense.........          668       638      2,674      2,552        764       612       789
                                   --------  --------   --------   --------   --------   -------   -------
         Fixed charges........     $ 12,800  $ 14,388   $ 60,047   $ 43,570   $ 11,466   $ 3,131   $ 2,816
                                   ========  ========   ========   ========   ========   =======   =======
Ratio of earnings to fixed
  charges.....................          9.4       8.3        8.4        5.1       11.1      24.4       8.3
                                   ========  ========   ========   ========   ========   =======   =======
</TABLE>

<PAGE>

                                                                    EXHIBIT 23.1


                        CONSENT OF INDEPENDENT AUDITORS

We consent to the reference to our firm under the caption "Experts" in the Post-
Effective Amendment No. 1 to the Registration Statement (Form S-3, No. 333-
24457) of Transocean Offshore Inc., a Cayman Islands exempted company, and to
the incorporation by reference therein of our report dated January 26, 1999,
with respect to the consolidated financial statements of Transocean Offshore
Inc., a Delaware corporation, included in its Annual Report (Form 10-K) for the
year ended December 31, 1998, filed with the Securities and Exchange Commission.


                                         /s/ Ernst & Young LLP

Houston, Texas
June  24, 1999

<PAGE>

                                                                      EXHIBIT 24


                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall
<PAGE>

deem necessary or incidental in connection therewith, and to file the same with
the Commission and to appear before the Commission in connection with any matter
relating thereto.  Each of said attorneys shall have full power and authority to
do and perform in the name and on behalf of the undersigned, in any and all
premises, as fully and to all intents and purposes as the undersigned might or
could do in person, the undersigned hereby ratifying and approving the acts that
said attorneys and each of them, or their or his substitutes or substitute, may
lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                        /s/  W. Dennis Heagney
                                        -------------------------------
                                        Name: W. Dennis Heagney
<PAGE>

                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                        /s/ Richard D. Kinder
                                        -------------------------------
                                        Name: Richard D. Kinder
<PAGE>

                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                         /s/ Ronald L. Kuehn, Jr.
                                         ------------------------------
                                         Name: Ronald L. Kuehn, Jr.
<PAGE>

                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                         /s/ Robert J. Lanigan
                                         --------------------------------
                                         Name: Robert J. Lanigan
<PAGE>

                            TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                         /s/ Fridtjof Lorentzen
                                         --------------------------------
                                         Name: Fridtjof Lorentzen
<PAGE>

                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                         /s/ Max L. Lukens
                                         --------------------------------
                                         Name: Max L. Lukens
<PAGE>

                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                         /s/ Martin B. McNamara
                                         --------------------------------
                                         Name: Martin B. McNamara
<PAGE>

                           TRANSOCEAN OFFSHORE INC.

                               Power of Attorney

     WHEREAS, TRANSOCEAN OFFSHORE INC., a Cayman Islands exempted company
limited by shares (the "Company"), intends to file with the Securities and
Exchange Commission (the "Commission") pursuant to the Securities Act of 1933,
as amended (the "Securities Act"), and as contemplated by Rule 414 thereunder,
post-effective amendments to the following Registration Statements:

     .    Form S-8 (Employee Stock Purchase Plan) (Registration No. 333-58203);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 333-58211);

     .    Form S-8 (Sonat Offshore Drilling Savings Plan) (Registration
          No. 33-66036);

     .    Form-S-8 (Long Term Incentive Plan) (Registration No. 333-12475);

     .    Form S-8 (Long Term Incentive Plan) (Registration No. 33-64776);

     .    Form S-3 (Shelf Registration) (Registration No. 333-24457);

     .    Form S-3 (Shelf Registration) (Registration No. 333-59001);

each including a related prospectus or prospectuses, with such further
amendment(s) thereto (including further post-effective amendments) and any
supplement(s) thereto (collectively, the "Post-Effective Amendments"), as
prescribed by the Commission pursuant to the Securities Act and the rules and
regulations thereunder, together with any and all exhibits and other documents
relating to the Post-Effective Amendments, in each case as may be necessary or
appropriate in connection with the registration of ordinary shares, par value
U.S. $.01 per share, of the Company;

     NOW THEREFORE, the undersigned, in his capacity as a director or officer or
both, as the case may be, of the Company, does hereby appoint J. Michael
Talbert, Robert L. Long, Eric B. Brown, Barbara S. Koucouthakis and Nicholas J.
Evanoff, and each of them severally, his true and lawful attorney or attorneys
with power to act with or without the others, and with full power of
substitution and resubstitution, to execute in his name, place and stead, in his
capacity as director, officer or both, as the case may be, of the Company, the
Post-Effective Amendments, including the exhibits thereto and the prospectus or
prospectuses referred to above, and any and all amendments thereto (including
further post-effective amendments) and any registration statement for the same
offering filed pursuant to Rule 462 under the Securities Act and any
supplement(s) thereto and any and all instruments necessary or incidental in
connection therewith, as said attorney or attorneys shall deem necessary or
incidental in connection therewith, and to file the same with the Commission and
to appear before the Commission in connection with any matter relating thereto.
Each of said attorneys shall have full power and authority to do and perform in
the name and on behalf of the
<PAGE>

undersigned, in any and all premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby ratifying
and approving the acts that said attorneys and each of them, or their or his
substitutes or substitute, may lawfully do or cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has executed this power of attorney as
of the 17th day of May, 1999.


                                         /s/ Kristian Siem
                                         --------------------------------
                                         Name: Kristian Siem


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