<PAGE>   1
                                                                    EXHIBIT 10.2


                                AMENDMENT NO. 2

  THIS AMENDMENT, dated as of April 9, 1998 (this "Amendment"), to the Second
Amended and Restated Credit Agreement, dated as of March 23, 1995, as amended
and restated through December 13, 1996 (as amended, supplemented or otherwise
modified prior to the date hereof, the "Credit Agreement"), among LEVIATHAN GAS
PIPELINE PARTNERS, L.P., a Delaware limited partnership (the "Borrower"), the
banks and other financial institutions (the "Lenders") parties hereto, THE
CHASE MANHATTAN BANK, a New York banking corporation, as administrative agent
(in such capacity, the "Administrative Agent") for the Lenders and ING (U.S.)
CAPITAL CORPORATION, a Delaware corporation, as co-arranger for the Lenders
(the "Co-Arranger").

                              W I T N E S S E T H:

  WHEREAS, DeepTech International Inc. ("DeepTech"), which indirectly owns
approximately 27% of the Borrower and 85% of Leviathan Gas Pipeline Company,
the sole general partner of the Borrower, has entered into the Agreement and
Plan of Merger (the "Merger Agreement,") with El Paso Natural Gas Company ("El
Paso") pursuant to which DeepTech will merge with El Paso or a subsidiary of El
Paso (the "Merger"); and

  WHEREAS, the completion of the Merger is subject to the consummation of
certain related transactions (the "Related Transactions") by DeepTech and/or
some of its subsidiaries, including the Borrower; and

  WHEREAS, in connection with the Merger, the Related Transactions and other
matters, the Borrower has requested that the Administrative Agent, the
Co-Arranger and the Lenders amend the Credit Agreement and waive the applicable
provisions of the Credit Agreement to (i) permit the Borrower and certain of
its subsidiaries to perform its or their obligations under the Redemption
Agreement dated February 27, 1998 (the "Redemption Agreement") between Tatham
offshore, Inc.  ("TOFF") and Flextrend Development Company, L.L.C., and (ii)
ensure that the consummation of the Merger and the Related Transactions and
certain other matters (including the automatic acceleration of certain options
under, and in accordance with, the Leviathan Unit Rights Appreciation Plan as a
result of a change in control as provided therein, do not cause or result in a
violation or breach of or a Default or Event of Default under the Credit
Agreement; and

  WHEREAS, the Administrative Agent, the Co-Arranger and the Required Lenders
are willing to agree to such amendments and waivers, but only on the terms and
subject to the conditions set forth in this Amendment;

  NOW, THEREFORE, in consideration of the premises and for other good and
valuable consideration, the sufficiency of which is hereby acknowledged, the
Borrower, the Administrative Agent, the Co-Arranger and the Required Lenders
hereby agree as follows:



                                       1
<PAGE>   2

         1.      Definitions.  Unless other wise defined herein, terms defined
in the recitals to this Amendment have the meanings specified therein, and
terms defined in the Credit Agreement (including all amendments thereto) are
used herein as therein defined.

         2.      Amendments and Waivers to Credit Agreement.

                 (a)      Amendments to Section 1.  Subsection 1.1 of the
Credit Agreement is amended as follows:

                          (i)     The definition of "Change of Control" is
amended by deleting the phrase "(other than management of DeepTech as of the
Closing Date and the shareholders of DeepTech as of the Closing Date)" and
substituting therefor the following phrase;

                          (other than the management of DeepTech as of the
                          Closing Date, the shareholders of DeepTech as of the
                          Closing Date and El Paso Natural Gas Company or any
                          Person controlling El Paso Natural Gas Company or any
                          successor of any such Person or El Paso Natural Gas
                          Company pursuant to a merger or consolidation with a
                          sole surviving entity)

                          (ii)    The definition of "Incurrence Limitation" is
amended by deleting from clause (b) (i) thereof the amount "3.25" and
substituting therefor the phrase "Incurrence Limitation Factor".

                          (iii)   The following definition is added to
Subsection 1.1 of the Credit Agreement in proper alphabetical order:

                          "Incurrence Limitation Factor": (a) from the
                          Amendment Effective Date (as defined in the Amendment
                          dated as of April 9, 1998 to this Agreement) to
                          December 31, 1998, 4.50, (b) thereafter to March 31,
                          1999, 4.25, (c) thereafter to June 30, 1999, 4.00,
                          (d) thereafter to September 30, 1999, 3.75 and (e)
                          thereafter, 3.50.

                 (b)      Amendment to Section 7.  Subsection 7.2(c) of the
Credit Agreement is hereby amended by adding at the end thereof the phrase ",
provided that such projections and certificate in respect of fiscal year 1998
may be delivered on or prior to April 15, 1998."

                 (c)      Amendments to Section 8.  Subsection 8.1 of the
Credit Agreement shall be amended as follows:

                          (i)     Subsection 8.1(a) of the Credit Agreement is
hereby amended by deleting the amount "$125,000,000" and substituting therefor
the amount "$85,000,000".

                          (ii)    Subsection 8.1(b) of the Credit Agreement is
hereby deleted.



                                       2
<PAGE>   3
                          (iii)   Subsection 8.1(d)(ii) of the Credit Agreement
         is hereby amended by deleting therefrom the phrase "3.25" and
         substituting therefor the phrase "the Incurrence Limitation Factor".

                          (iv)    Subsection 8.1(e)(ii) of the Credit Agreement
         is hereby amended by deleting the phrase "4.0" and substituting
         therefor the phrase "the Incurrence Limitation Factor".

                          (v)     Subsection 8.6 of the Credit Agreement is
         hereby amended by (a) deleting the "and" from the end of clause (c),
         (b) deleting the period from the end of clause (d) and substituting
         therefor the phrase "; and " and (c) adding the following new clause
         (e):

                          (e) the Borrower may permit the redemption of the
                          7,500 shares of 9% Senior Convertible Preferred Stock
                          issued by Tatham Offshore, Inc. ("TOI") in exchange
                          for TOI's working interest in VK817, its 37.5%
                          working interest in West Delta 35 and its 100%
                          ownership of the Ship Shoal 331 Platform (and upon
                          such redemption the Lenders' security interest in
                          such Preferred Stock will terminate in accordance
                          with subsection 11.18).

         3.      Conditions to Effectiveness.  This Amendment shall become
effective on the date (the "Amendment Effective Date") on which all of the
following conditions precedent have been satisfied or waived:

                 (a)      The Borrower, the Administrative Agent and the
Required Lenders shall have executed and delivered to the Administrative Agent
this Amendment, and the other Loan Parties shall have executed and delivered to
the Administrative Agent the attached Acknowledgment approving this Amendment.

                 (b)      The Administrative Agent shall have received from the
Borrower (i) for the account of each Lender which executes and delivers this
Amendment prior to April 14, 1998, an amendment fee equal to .05% of such
Lender's Revolving Credit Commitment on the Amendment Effective Date and (ii)
for the  account of the Administrative Agent and the Co-Arranger, such fees as
are separately agreed with the Borrower.

         4.      General.

                 (a)      Representations and Warranties.  After giving effect
to the effectiveness of this Amendment, the representations and warranties made
by the Loan Parties in the Loan Documents are true and correct in all material
respects on and as of the Amendment Effective Date (unless such representations
or warranties are stated to refer to a specific earlier date, in which case
such representations and warranties shall be true and correct in all material
respects as of such earlier date) as if made on and as of the Amendment
Effective Date and no Default or Event of Default will have occurred and be
continuing.



                                       3
<PAGE>   4
                 (b)      Payment of Expenses.  The Borrower agrees to pay or
reimburse the Administrative Agent for all of its out-of-pocket costs and
reasonable expenses incurred in connection with this Amendment, any other
documents prepared in connection herewith and the transactions contemplated
hereby, including, without limitation, the reasonable fees and disbursements of
counsel to the Administrative Agent.

                 (c)      No Other Amendments; Confirmation.  Except as
expressly amended, modified and supplemented hereby, the provisions of the
Credit Agreement, the Notes and the other Loan Documents are and shall remain
in full force and effect.

                 (d)      Governing Law; Counterparts.        (I)  THIS
AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HERETO SHALL BE
GOVERNED BY, AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE
STATE OF NEW YORK.

                          (ii)    This Amendment may be executed by one or more
of the parties to this Amendment on any number of separate counterparts, and
all of said counterparts taken together shall be deemed to constitute one and
the same instrument.



                                       4
<PAGE>   5
         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed and delivered as of the day and year first above written.



                                           LEVIATHAN GAS PIPELINE PARTNERS, L.P.


                                           By
                                              ----------------------------------
                                              Name:     Keith Forman
                                              Title:    Chief Financial Officer


                                           THE CHASE MANHATTAN BANK, as 
                                           Administrative Agent and Lender


                                           By 
                                              ----------------------------------
                                              Name:
                                              Title:


                                           ING (U.S.) CAPITAL CORPORATION, as 
                                           Co-Arranger and Lender


                                           By 
                                              ----------------------------------
                                              Name:
                                              Title:


                                           DEN NORSKE BANK AS


                                           By 
                                              ----------------------------------
                                              Name:
                                              Title:


                                           WELLS FARGO BANK TEXAS, N.A.


                                           By
                                              ----------------------------------
                                              Name:
                                              Title:




                                       5
<PAGE>   6


                                           MEESPIERSON N.V.


                                           By
                                             ----------------------------------

                                              Name:
                                              Title:


                                           BANK OF SCOTLAND


                                           By                            
                                             ----------------------------------
                                              Name:
                                              Title:


                                           BANQUE PARIBAS


                                           By                             
                                             ----------------------------------
                                              Name:
                                              Title:


                                           By                              
                                             ----------------------------------
                                              Name:
                                              Title:


                                           CREDIT LYONNAIS CAYMAN ISLAND BRANCH


                                           By                            
                                             ----------------------------------
                                              Name:
                                              Title:


                                           FIRST UNION NATIONAL BANK OF NORTH 
                                           CAROLINA


                                           By                              
                                             ----------------------------------
                                              Name:
                                              Title:




                                       6
<PAGE>   7
                                           ARAB BANKING CORPORATION (B.S.C.)


                                           By
                                             ----------------------------------
                                              Name:
                                              Title:


                                           CREDIT AGRICOLE


                                           By                          
                                             ----------------------------------
                                              Name:
                                              Title:


                                           PNC BANK, NATIONAL ASSOCIATION


                                           By                             
                                             ----------------------------------
                                              Name:
                                              Title:


                                           THE BANK OF NOVA SCOTIA


                                           By                                
                                             ----------------------------------
                                              Name:
                                              Title:


                                           HIBERNIA NATIONAL BANK


                                           By                                 
                                             ----------------------------------
                                              Name:
                                              Title:



                                       7
<PAGE>   8
                                 ACKNOWLEDGMENT

         The undersigned guarantors hereby consent and agree to the foregoing
Amendment:


LEVIATHAN GAS PIPELINE COMPANY

By:                                                
   ----------------------------------
    Title:


DELOS OFFSHORE COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


EWING BANK GATHERING COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


FLEXTREND DEVELOPMENT COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


GREEN CANYON PIPELINE COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


LEVIATHAN OIL TRANSPORT SYSTEMS, L.L.C.

By:                                                
   ----------------------------------
    Title:


MANTA RAY GATHERING COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:




                                       8
<PAGE>   9


POSEIDON PIPELINE COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


SAILFISH PIPELINE COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


STINGRAY HOLDING, L.L.C.

By:                                                
   ----------------------------------
    Title:


TARPON TRANSMISSION COMPANY

By:                                                
   ----------------------------------
    Title:


TRANSCO HYDROCARBONS COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


TEXAM OFFSHORE GAS TRANSMISSION, L.L.C.

By:                                                
   ----------------------------------
    Title:


TRANSCO OFFSHORE PIPELINE COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:



                                       9
<PAGE>   10


VK DEEPWATER GATHERING COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:


VK-MAIN PASS GATHERING COMPANY, L.L.C.

By:                                                
   ----------------------------------
    Title:



                                       10