<PAGE>

                                                                     EXHIBIT 4.1
                  SECOND AMENDMENT TO SECURED CREDIT AGREEMENT

     THIS SECOND AMENDMENT TO SECURED CREDIT AGREEMENT (this "Amendment") dated
as of August 13, 1999, is by and among Transocean Enterprise Inc., a Delaware
corporation (the "Borrower"), the lenders from time to time parties hereto (each
a "Lender" and collectively, the  "Lenders"), ABN AMRO Bank N.V. ("ABN AMRO"), a
Netherlands chartered bank, as agent for the Lenders (in such capacity, the
"Agent"), and Australia and New Zealand Banking Group Limited, Bank of Montreal,
The Bank of Nova Scotia, Atlanta Agency, The Bank of Tokyo-Mitsubishi, Ltd.,
Houston Agency and Westdeutsche Landesbank Girozentrale, as co-agents for the
Lenders (in such capacity, collectively, the "Co-Agents").

                                   WITNESSETH
                                   ----------

     WHEREAS, the Borrower, the Lenders, the Agent and the Co-Agents have
entered into that certain Secured Credit Agreement dated as of January 17, 1997,
as amended by First Amendment to Secured Credit Agreement dated December 21,
1998 (such agreement, as amended, "Credit Agreement"), pursuant to which the
Lenders have made and agreed to make Loans to the Borrower; and

     WHEREAS, the Borrower, the Lenders, the Agent and the Co-Agents desire to
amend the Credit Agreement as hereinafter set forth;

     NOW, THEREFORE, in consideration of the premises and the mutual agreements
herein contained, the Borrower, the Lenders, the Agent and the Co-Agents hereby
agree as follows:

     1.   AMENDMENTS TO CREDIT AGREEMENT.  (a)  Section 1.1 of the Credit
Agreement is hereby amended by amending:

     (i)  the definitions of "Acceptance Date", "Conversion Date" and "Maturity
     Date" by deleting "August 31, 1999" in each such definition and inserting
     "October 31, 1999" in lieu thereof; and

     (ii)  the definition of "Guarantor" to read as follows:

          "Guarantor" means Transocean Offshore Inc., a Cayman Islands exempted
          company, as successor by merger and conversion to Transocean Offshore
          Inc., a Delaware corporation.

(b)  Clause (z) of Section 2.7(c)(i) of the Credit Agreement is hereby amended
to read as follows: "(z) any change in the Conversion Date from October 31,
1999."

(c)  Section 3.1(a) of the Credit Agreement is hereby amended by deleting
"December 31, 1998" in such Section and inserting "October 31, 1999" in lieu
thereof.

(d)  Each of Sections 4.2(ii) and 6.18(c) of the Credit Agreement is hereby
amended by deleting "August 31, 1999" in such Sections and inserting "October
31, 1999" in lieu thereof.
<PAGE>

     2.   REAFFIRMATION OF REPRESENTATIONS AND WARRANTIES.  To induce the
Lenders, the Agent and the Co-Agents to enter into this Amendment, the Borrower
hereby reaffirms, as of the date hereof, that its representations and warranties
contained in the Credit Agreement are true and correct in all material respects
(except to the extent such representations and warranties are not so true and
correct in all material respects as a result of the transactions expressly
permitted under the Credit Agreement or under the other Credit Documents, or
relate solely to an earlier date) and additionally represents and warrants as
follows:

               (i) The execution and delivery by the Borrower of this Amendment
     and the performance by the Borrower of its obligations under this Amendment
     and the Credit Agreement, as amended hereby, are within the Borrower's
     corporate powers, have been duly authorized by all necessary corporate
     action of the Borrower and do not and will not contravene in any material
     respect any provision of applicable law or contravene or conflict with any
     provision of the certificate of incorporation, bylaws or any material
     agreements binding upon the Borrower, and the execution and delivery by the
     Borrower of this Amendment have received all necessary governmental
     approvals or other consents (if any shall be required);

               (ii) This Amendment and the Credit Agreement, as amended hereby,
     are legal, valid and binding obligations of the Borrower enforceable
     against the Borrower in accordance with their terms, subject as to
     enforcement only to bankruptcy, insolvency, reorganization, moratorium or
     other similar laws affecting the enforcement of creditors' rights generally
     and equitable principles;

               (iii)  There are no actions, suits, proceedings or counterclaims
     (including, without limitation, derivative or injunctive actions) pending
     or, to the knowledge of the Borrower, threatened against the Borrower or
     any of its Subsidiaries which purports to affect the legality, validity or
     enforceability of this Amendment, the Credit Agreement, as amended hereby,
     or any other Credit Document; and

               (iv) No Default or Event of Default has occurred and is
     continuing (after giving effect to this Amendment).

     3.   REAFFIRMATION OF CREDIT AGREEMENT.  This amendment shall be deemed to
be an amendment to the Credit Agreement, and the Credit Agreement, as amended
hereby, is hereby ratified, approved and confirmed in each and every respect.
All references to the Credit Agreement in the Credit Agreement and the other
Credit Documents (excluding this Amendment) shall hereafter be deemed to refer
to the Credit Agreement, as amended hereby.  The parties hereto hereby
undertake, in good faith, to amend any other Credit Documents necessary so as to
reflect the agreements of the parties set forth in this Amendment.

     4.   DEFINED TERMS.  Terms used but not defined herein when defined in the
Credit Agreement shall have the same meanings herein unless the context
otherwise requires.

                                      -2-
<PAGE>

     5.   CONDITIONS PRECEDENT TO EFFECTIVENESS OF AMENDMENT.  The effectiveness
of this Amendment is subject to receipt by the Agent of the following documents,
all in form and substance reasonably satisfactory to the Agent:

               (i) Transocean Performance Guaranty.  Ratification by Transocean
     of its obligations under the Second Amended and Restated Transocean
     Performance Guaranty in substantially the form of Exhibit A; and

               (ii) Other Documents.  Such other documents as the Agent may
     reasonably request.

     6.   GOVERNING LAW; SUBMISSION TO JURISDICTION; WAIVER OF JURY TRIAL.

          (a) This Amendment and the other Credit Documents, and the rights and
duties of the parties hereto and thereto, shall be construed in accordance with
and governed by the internal laws of the state of New York.

          (b) TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, THE PARTIES
HERETO AGREE THAT ANY LITIGATION BASED HEREON, OR ARISING OUT OF, UNDER, OR IN
CONNECTION WITH, THIS AMENDMENT OR ANY OTHER CREDIT DOCUMENT, OR ANY COURSE OF
CONDUCT, COURSE OF DEALING, STATEMENT (WHETHER VERBAL OR WRITTEN) OR ACTIONS OF
THE AGENT, THE CO-AGENTS, THE LENDERS OR THE BORROWER MAY BE BROUGHT AND
MAINTAINED IN THE COURTS OF THE STATE OF NEW YORK SITTING IN THE BOROUGH OF
MANHATTAN OR THE UNITED STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF NEW
YORK.  TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, THE BORROWER HEREBY
EXPRESSLY AND IRREVOCABLY SUBMITS TO THE JURISDICTION OF THE COURTS OF THE STATE
OF NEW YORK AND THE UNITED STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF
NEW YORK FOR THE PURPOSE OF ANY SUCH LITIGATION AS SET FORTH ABOVE AND
IRREVOCABLY AGREES TO BE BOUND BY AND ANY JUDGMENT RENDERED THEREBY IN
CONNECTION WITH SUCH LITIGATION.  TO THE FULLEST EXTENT PERMITTED BY APPLICABLE
LAW, THE BORROWER FURTHER IRREVOCABLY CONSENTS TO THE SERVICE OF PROCESS, BY
REGISTERED MAIL, POSTAGE PREPAID, OR BY PERSONAL SERVICE WITHIN OR WITHOUT THE
STATE OF NEW YORK.  TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, THE
BORROWER HEREBY EXPRESSLY AND IRREVOCABLY WAIVES, ANY OBJECTION WHICH IT MAY
HAVE OR HEREAFTER MAY HAVE TO THE LAYING OF VENUE OF ANY SUCH LITIGATION BROUGHT
IN ANY SUCH COURT REFERRED TO ABOVE AND ANY CLAIM THAT ANY SUCH LITIGATION HAS
BEEN BROUGHT IN AN INCONVENIENT FORUM.  TO THE EXTENT THAT THE BORROWER HAS OR
HEREAFTER MAY ACQUIRE ANY IMMUNITY FROM JURISDICTION OF ANY COURT OR FROM ANY
LEGAL PROCESS (WHETHER THROUGH SERVICE OF NOTICE, ATTACHMENT PRIOR TO JUDGMENT,
ATTACHMENT IN AID OF EXECUTION OR OTHERWISE) WITH RESPECT TO ITSELF OR ITS
PROPERTY, THE BORROWER HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT

                                      -3-
<PAGE>

PERMITTED BY APPLICABLE LAW, SUCH IMMUNITY IN RESPECT OF ITS OBLIGATIONS UNDER
THIS AMENDMENT AND THE OTHER CREDIT DOCUMENTS.

          (c) TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, EACH PARTY
HERETO WAIVES ANY RIGHT TO A TRIAL BY JURY IN ANY ACTION OR PROCEEDING TO
ENFORCE OR DEFEND ANY RIGHTS UNDER THIS AMENDMENT, THE CREDIT AGREEMENT, ANY
OTHER CREDIT DOCUMENT OR UNDER ANY AMENDMENT, INSTRUMENT, DOCUMENT OR AGREEMENT
DELIVERED OR WHICH MAY IN THE FUTURE BE DELIVERED IN CONNECTION HEREWITH OR
THEREWITH OR ARISING FROM ANY BANKING RELATIONSHIP EXISTING IN CONNECTION WITH
THIS AMENDMENT, THE CREDIT AGREEMENT, ANY OTHER CREDIT DOCUMENT OR UNDER ANY
AMENDMENT, INSTRUMENT, DOCUMENT OR AGREEMENT DELIVERED OR WHICH MAY IN THE
FUTURE BE DELIVERED IN CONNECTION HEREWITH OR THEREWITH AND AGREES THAT ANY SUCH
ACTION OR PROCEEDING SHALL BE TRIED BEFORE A COURT AND NOT BEFORE A JURY.

     7.   Counterparts.  This Amendment may be executed in any number of
counterparts, and by the different parties on different counterpart signature
pages, each of which when executed shall be deemed an original, but all such
counterparts taken together shall constitute one and the same agreement.

     8.   Severability.  Any provision of this Amendment that is prohibited or
unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective
to the extent of such prohibition or unenforceability without invalidating the
remaining provisions hereof, and any such prohibition or unenforceability in any
jurisdiction shall not invalidate or render unenforceable such provision in any
other jurisdiction.

     9.   Headings.  Section headings used in this Amendment are for reference
only and shall not affect the construction of this Amendment.

     10.  NOTICE OF ENTIRE AGREEMENT.  This Amendment, together with the other
Credit Documents, constitute the entire understanding among the Borrower, the
Lenders, the Agent and the Co-Agents and supersede all earlier or
contemporaneous agreements, whether written or oral, concerning the subject
matter of the Credit Documents.  THIS WRITTEN AMENDMENT, TOGETHER WITH THE OTHER
CREDIT DOCUMENTS, REPRESENTS THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT
BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES.  THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.

                                      -4-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have entered into this Second
Amendment to Secured Credit Agreement as of the date first written above.

                         BORROWER:
                         --------

                         TRANSOCEAN ENTERPRISE INC.,
                         a Delaware corporation



                         By:    /s/ Brian C. Voegele
                            ---------------------------------------------------
                         Name:  Brian C. Voegele
                              -------------------------------------------------
                         Title: Vice President - Finance
                               ------------------------------------------------

                         LENDERS:
                         -------

                         ABN AMRO BANK N.V., as Agent, Collateral
                         Agent and as a Lender


                         By:    /s/ Stuart Murray
                            ---------------------------------------------------
                         Name:  Stuart Murray
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------

                         By:    /s/ Charles W. Randall
                            ---------------------------------------------------
                         Name:  Charles W. Randall
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------


                         AUSTRALIA AND NEW ZEALAND BANKING
                         GROUP LIMITED, as Co-Agent and as a Lender


                         By:    /s/ Claude Devillers
                            ---------------------------------------------------
                         Name:  Claude Devillers
                              -------------------------------------------------
                         Title: Director - Oil and Gas Americas
                               ------------------------------------------------

                                      -5-
<PAGE>

                         BANK OF MONTREAL, as Co-Agent and as a Lender


                         By:    /s/ Mary Lee Latta
                            ---------------------------------------------------
                         Name:  Mary Lee Latta
                              -------------------------------------------------
                         Title: Director - Bank of Montreal
                               ------------------------------------------------

                         THE BANK OF NOVA SCOTIA, ATLANTA
                         AGENCY, as Co-Agent and as a Lender


                         By:    /s/ F.C.H. Ashby
                            ---------------------------------------------------
                         Name:  F.C.H. Ashby
                              -------------------------------------------------
                         Title: Senior Manager - Loan Operations
                               ------------------------------------------------


                         THE BANK OF TOKYO-MITSUBISHI, LTD.,
                         HOUSTON AGENCY, as Co-agent and as a Lender


                         By:    /s/ Michael Heiss
                            ---------------------------------------------------
                         Name:  Michael Heiss
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------


                         WESTDEUTSCHE LANDESBANK GIROZENTRALE,
                         as Co-Agent and as a Lender


                         By:    /s/ Jonathan Berman
                            ---------------------------------------------------
                         Name:  Jonathan Berman
                              -------------------------------------------------
                         Title: Managing Director
                               ------------------------------------------------


                         By:    /s/ Cheryl A. Solometo
                            ---------------------------------------------------
                         Name:  Cheryl A. Solometo
                              -------------------------------------------------
                         Title: Managing Director
                               ------------------------------------------------

                                      -6-
<PAGE>

                         BAYERISCHE HYPO-UND VEREINSBANK AG,
                         New York Branch, as a Lender


                         By:    /s/ Pamela J. Gillons
                            ---------------------------------------------------
                         Name:  Pamela J. Gillons
                              -------------------------------------------------
                         Title: Associate Director
                               ------------------------------------------------


                         By:    /s/ Steven Atwell
                            ---------------------------------------------------
                         Name:  Steven Atwell
                              -------------------------------------------------
                         Title: Director
                               ------------------------------------------------


                         CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
                         as a Lender

                         By:    /s/ Ki Allen
                            ---------------------------------------------------
                         Name:  Ki Allen
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------


                         SUNTRUST BANK, ATLANTA, as a Lender

                         By:    /s/ John A. Fields, Jr.
                            ---------------------------------------------------
                         Name:  John A. Fields, Jr.
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------


                         By:    /s/ Steven J. Newby
                            ---------------------------------------------------
                         Name:  Steven J. Newby
                              -------------------------------------------------
                         Title: Assistant Vice  President
                               ------------------------------------------------

                                      -7-
<PAGE>

                         DEUTSCHE BANK AG IN HAMBURG, as a Lender



                         By:    /s/ Ehrhardt
                            ---------------------------------------------------
                         Name:  Ehrhardt
                              -------------------------------------------------
                         Title: Senior Vice President
                               ------------------------------------------------

                         By:    /s/ L. Peter Flug
                            ---------------------------------------------------
                         Name:  L. Peter Flug
                              -------------------------------------------------
                         Title: Legal Counsel
                               ------------------------------------------------


                         THE FIRST NATIONAL BANK OF CHICAGO, as a Lender


                         By:    /s/ Karen A. Patterson
                            ---------------------------------------------------
                         Name:  Karen A. Patterson
                              -------------------------------------------------
                         Title: Authorized Officer
                               ------------------------------------------------


                         THE BANK OF NEW YORK, as a Lender


                         By:    /s/ Peter Keller
                            ---------------------------------------------------
                         Name:  Peter Keller
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------


                         DG BANK DEUTSCHE GENOSSENSCHAFTSBANK, AG,  as Lender


                         By:    /s/ Mark K. Connelly
                            ---------------------------------------------------
                         Name:  Mark K. Connelly
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------

                         By:    /s/ Lynne McCarthy
                            ---------------------------------------------------
                         Name:  Lynne McCarthy
                              -------------------------------------------------
                         Title: Assistant Vice President
                               ------------------------------------------------

                                      -8-
<PAGE>

                         ROYAL BANK OF CANADA, as a Lender


                         By:    /s/ Linda M. Stephens
                            ---------------------------------------------------
                         Name:  Linda M. Stephens
                              -------------------------------------------------
                         Title: Senior Manager
                               ------------------------------------------------


                         KBC BANK, N.V., as a Lender


                         By:    /s/ Robert Snauffer
                            ---------------------------------------------------
                         Name:  Robert Snauffer
                              -------------------------------------------------
                         Title: First Vice President
                               ------------------------------------------------

                         By:    /s/ Declan Meagher
                            ---------------------------------------------------
                         Name:  Declan Meagher
                              -------------------------------------------------
                         Title: First Vice President
                               ------------------------------------------------


                         THE ROYAL BANK OF SCOTLAND plc, as a Lender


                         By:    /s/ Scott Barton
                            ---------------------------------------------------
                         Name:  Scott Barton
                              -------------------------------------------------
                         Title: Vice President
                               ------------------------------------------------

                                      -9-