<PAGE>   1
===============================================================================



                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 10-Q


              [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                  FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1998

                                       OR

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                  FOR THE TRANSITION PERIOD FROM _____ TO _____

                           COMMISSION FILE NO. 1-11680


                      LEVIATHAN GAS PIPELINE PARTNERS, L.P.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)


       DELAWARE                                                76-0396023
(STATE OF ORGANIZATION)                                     (I.R.S. EMPLOYER
                                                          IDENTIFICATION NO.)

                                   600 TRAVIS
                                   SUITE 7200
                              HOUSTON, TEXAS 77002
          (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES, INCLUDING ZIP CODE)

                                 (713) 224-7400
              (REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE)



    INDICATE BY CHECK MARK WHETHER THE REGISTRANT: (1) HAS FILED ALL REPORTS
REQUIRED TO BE FILED BY SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF
1934 DURING THE PRECEDING TWELVE MONTHS (OR FOR SUCH SHORTER PERIOD THAT THE
REGISTRANT WAS REQUIRED TO FILE SUCH REPORTS), AND (2) HAS BEEN SUBJECT TO SUCH
FILING REQUIREMENTS FOR THE PAST 90 DAYS. YES X   NO
                                             ---     ---

===============================================================================
<PAGE>   2
                      LEVIATHAN GAS PIPELINE PARTNERS, L.P.
                                AND SUBSIDIARIES

                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                           Page
                                                                           ----
<S>                                                                        <C>
PART I.   FINANCIAL INFORMATION..............................................1

ITEM 1.  CONSOLIDATED FINANCIAL STATEMENTS:
    Consolidated Balance Sheet as of March 31, 1998 (unaudited)
      and December 31, 1997..................................................1
    Unaudited Consolidated Statement of Operations for the
      Three Months Ended March 31, 1998 and 1997, respectively...............2
    Unaudited Consolidated Statement of Cash Flows for the
      Three months Ended March 31, 1998 and 1997.............................3
    Consolidated Statement of Partners' Capital for the Three months
      Ended March 31, 1998 (unaudited).......................................4
    Notes to Consolidated Financial Statements (unaudited)...................5

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF
   FINANCIAL CONDITION AND RESULTS OF OPERATIONS.............................11

PART II.   OTHER INFORMATION.................................................16

    Item 1.  Legal Proceedings
    Item 2.  Changes in Securities and Use of Proceeds
    Item 3.  Defaults Upon Senior Securities
    Item 4.  Submission of Matters to a Vote of Security Holders
    Item 5.  Other Information
    Item 6.  Exhibits and Reports on Form 8-K

SIGNATURES...................................................................17
</TABLE>



                                       i
<PAGE>   3

                          PART I. FINANCIAL INFORMATION

ITEM 1.  CONSOLIDATED FINANCIAL STATEMENTS.

             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                              March 31,     December 31,
                                                                                1998           1997
                                                                              ---------      ---------
    ASSETS                                                                  (unaudited)
<S>                                                                        <C>                 <C>
Current assets:
    Cash and cash equivalents                                                 $   1,264      $   6,430
    Accounts receivable                                                           1,531          1,953
    Accounts receivable from affiliates                                           5,245          6,608
    Other current assets                                                            595            653
                                                                              ---------      ---------
       Total current assets                                                       8,635         15,644
                                                                              ---------      ---------

Equity investments                                                              184,664        182,301
                                                                              ---------      ---------

Property and equipment:
    Pipelines                                                                    76,680         78,244
    Platforms and facilities                                                    112,606         97,882
    Oil and gas properties, at cost, using successful efforts method            120,339        120,296
                                                                              ---------      ---------
                                                                                309,625        296,422
    Less accumulated depreciation, depletion, amortization and impairment       103,134         95,783
                                                                              ---------      ---------
       Property and equipment, net                                              206,491        200,639
                                                                              ---------      ---------

Investment in Tatham Offshore, Inc. (Note 2)                                      7,500          7,500
Other noncurrent assets                                                           3,510          3,758
                                                                              ---------      ---------

       Total assets                                                           $ 410,800      $ 409,842
                                                                              =========      =========

   LIABILITIES AND PARTNERS' CAPITAL

Current liabilities:
    Accounts payable and accrued liabilities                                  $  15,040      $  12,522
    Accounts payable to affiliates                                                  770          1,032
                                                                              ---------      ---------
       Total current liabilities                                                 15,810         13,554
Deferred federal income taxes                                                     1,267          1,399
Notes payable                                                                   251,000        238,000
Other noncurrent liabilities                                                     15,369         13,304
                                                                              ---------      ---------
       Total liabilities                                                        283,446        266,257
                                                                              ---------      ---------

Minority interest                                                                  (543)          (381)
                                                                              ---------      ---------

Partners' capital                                                               127,897        143,966
                                                                              ---------      ---------

       Total liabilities and partners' capital                                $ 410,800      $ 409,842
                                                                              =========      =========
</TABLE>


The accompanying notes are an integral part of this financial statement.

                                       1
<PAGE>   4
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
                 UNAUDITED CONSOLIDATED STATEMENT OF OPERATIONS
                     (In thousands, except per Unit amounts)

<TABLE>
<CAPTION>
                                                                Three Months Ended
                                                                    March 31,
                                                              ---------------------
                                                                1998          1997
                                                              --------      --------
<S>                                                          <C>               <C>
Revenue:
   Oil and gas sales                                          $  9,135      $ 18,100
   Gathering, transportation and platform services               3,260         5,839
   Equity in earnings                                            5,319         7,089
                                                              --------      --------
                                                                17,714        31,028
                                                              --------      --------

Costs and expenses:
   Operating expenses                                            2,837         3,103
   Depreciation, depletion and amortization                      7,867        13,945
   General and administrative expenses and management fee        4,950         2,473
                                                              --------      --------
                                                                15,654        19,521
                                                              --------      --------

Operating income                                                 2,060        11,507
Interest income and other                                           84           693
Interest and other financing costs                              (3,722)       (3,112)
Minority interest in income                                         13           (90)
                                                              --------      --------
(Loss) income before income taxes                               (1,565)        8,998
Income tax (benefit) expense                                      (141)           34
                                                              --------      --------

Net (loss) income                                             $ (1,424)     $  8,964
                                                              ========      ========

Weighted average number of Units outstanding                    24,367        24,367
                                                              ========      ========

Basic and diluted net (loss) income per Unit                  $  (0.05)     $   0.32
                                                              ========      ========
</TABLE>


The accompanying notes are an integral part of this financial statement.


                                       2
<PAGE>   5

             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
                 UNAUDITED CONSOLIDATED STATEMENT OF CASH FLOWS
                                 (In thousands)


<TABLE>
<CAPTION>
                                                                                Three Months Ended
                                                                                    March 31,
                                                                             ------------------------
                                                                                1998         1997
                                                                             ----------   -----------
<S>                                                                         <C>           <C>
Cash flows from operating activities:
    Net (loss) income                                                        $ (1,424)     $  8,964
    Adjustments to reconcile net (loss) income to net cash
     provided by operating activities:
       Amortization of debt issue costs                                           240           241
       Depreciation, depletion and amortization                                 7,867        13,945
       Minority interest in income                                                (13)           90
       Equity in earnings                                                      (5,319)       (7,089)
       Distributions from equity investments                                    6,325         5,275
       Deferred income taxes                                                     (132)           31
       Other noncash items                                                      1,556        (4,006)
       Changes in operating working capital:
         Decrease (increase) in accounts receivable                               422          (547)
         Decrease in accounts receivable from affiliates                        1,363         4,298
         Decrease in other current assets                                          58           584
         Increase (decrease) in accounts payable and accrued liabilities        2,518        (7,133)
         Decrease in payable to affiliates                                       (262)       (1,778)
                                                                             --------      --------
              Net cash provided by operating activities                        13,199        12,875
                                                                             --------      --------

Cash flows from investing activities:
    Additions to pipelines, platforms and facilities                          (13,190)       (1,821)
    Equity investments                                                         (3,338)          (24)
    Development of oil and gas properties                                         (43)       (6,772)
                                                                             --------      --------
              Net cash used in investing activities                           (16,571)       (8,617)
                                                                             --------      --------

Cash flows from financing activities:
    Decrease in restricted cash                                                  --             716
    Proceeds from notes payable                                                23,000          --
    Repayments of notes payable                                               (10,000)       (8,000)
    Debt issue costs                                                             --             (98)
    Distributions to partners                                                 (14,794)      (10,326)
                                                                             --------      --------
              Net cash used in financing activities                            (1,794)      (17,708)
                                                                             --------      --------

Decrease in cash and cash equivalents                                          (5,166)      (13,450)
Cash and cash equivalents at beginning of year                                  6,430        16,489
                                                                             --------      --------
Cash and cash equivalents at end of period                                   $  1,264      $  3,039
                                                                             ========      ========

Cash paid for interest, net of amounts capitalized                           $  3,381      $  2,930
Cash paid for income taxes                                                   $   --        $      2
</TABLE>


The accompanying notes are an integral part of this financial statement.

                                       3
<PAGE>   6
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
                   CONSOLIDATED STATEMENT OF PARTNERS' CAPITAL
                                 (In thousands)

<TABLE>
<CAPTION>
                                           Preference       Common        General
                                          Unitholders     Unitholder      Partner       Total
                                          -----------     ----------      -------       -----
<S>                                      <C>              <C>            <C>            <C>
Partners' capital at
    December 31, 1997                    $ 163,426      $ (15,400)     $  (4,060)     $ 143,966

Net loss for the three months
    ended March 31, 1998 (unaudited)          (852)          (297)          (275)        (1,424)

Cash distributions (unaudited)              (9,038)        (3,146)        (2,461)       (14,645)
                                         ---------      ---------      ---------      ---------

Partners' capital at
    March 31, 1998 (unaudited)           $ 153,536      $ (18,843)     $  (6,796)     $ 127,897
                                         =========      =========      =========      =========

Limited partnership Units
    outstanding at December 31, 1997
    and March 31, 1998 (unaudited)          18,075          6,292         -- (a)         24,367
                                         =========      =========      =========      =========
</TABLE>
-----------------

   (a) Leviathan Gas Pipeline Company owns a 1% general partner interest in
Leviathan Gas Pipeline Partners, L.P.


The accompanying notes are an integral part of this financial statement.


                                       4
<PAGE>   7

             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)


NOTE 1 - ORGANIZATION AND BASIS OF PRESENTATION:

Leviathan Gas Pipeline Partners, L.P. (the "Partnership"), a publicly held
Delaware limited partnership, is primarily engaged in the gathering and
transportation of natural gas and crude oil through pipeline systems located in
the Gulf of Mexico (the "Gulf") and in the development and production of oil and
gas reserves. The Partnership's assets include interests in (i) eight natural
gas pipelines, (ii) a crude oil pipeline system, (iii) five strategically
located multi-purpose platforms, (iv) three producing oil and gas properties and
(v) a dehydration facility.

Leviathan Gas Pipeline Company ("Leviathan"), a Delaware corporation and
wholly-owned subsidiary of Leviathan Holdings Company ("Leviathan Holdings"), an
85%-owned subsidiary of DeepTech International Inc. ("DeepTech"), is the general
partner of the Partnership, and as such, performs all management and operational
functions of the Partnership and its subsidiaries. The remaining 15% of
Leviathan Holdings is principally owned by members of the management of
DeepTech. DeepTech also owns and controls several other operating subsidiaries
which are engaged in various oil and gas related activities.

As of March 31, 1998, the Partnership had 18,075,000 Preference Units and
6,291,894 Common Units outstanding. All of the Preference Units are owned by the
public, representing a 72.7% effective limited partner interest in the
Partnership. Leviathan, through its ownership of all of the Common Units, its 1%
general partner interest in the Partnership and its approximate 1% nonmanaging
interest in certain of the Partnership's subsidiaries, owns a 27.3% effective
interest in the Partnership (23.2% effective interest net to DeepTech's
interest). See Note 4 for a discussion of the conversion of Preference Units
into Common Units.

The accompanying consolidated financial statements have been prepared without
audit pursuant to the rules and regulations of the Securities and Exchange
Commission. Accordingly, the statements reflect all normal recurring adjustments
which are, in the opinion of management, necessary for a fair statement of the
results of operations for the period covered by such statements. These interim
financial statements should be read in conjunction with the audited consolidated
financial statements and notes thereto contained in the Partnership's Annual
Report on Form 10-K for the year ended December 31, 1997.

Effective January 1, 1998, the Partnership adopted Statement of Financial
Accounting Standard ("SFAS") No. 131, "Disclosures About Segments of an
Enterprise and Related Information". SFAS No. 131 establishes standards for the
method public entities report information about operating segments in both
interim and annual financial statements issued to shareholders and requires
related disclosures about products and services, geographic areas and major
customers. The Partnership is currently evaluating the disclosure requirements
of this statement as this statement does not apply to interim financial
statements in the initial year of its adoption. However, comparative financial
information for interim periods in the initial year of application must be
reported in financial statements for interim periods in the second year of
application.

NOTE 2 - RECENT EVENTS:

On March 2, 1998, DeepTech announced that its Board of Directors and holders of
a majority of its outstanding stock had approved the execution of an Agreement
and Plan of Merger (the "Merger Agreement") pursuant to which DeepTech would
merge (the "Merger") with El Paso Natural Gas Company ("El Paso") or, under
certain circumstances, one of its subsidiaries.

The material terms of the Merger and the transactions contemplated by the Merger
Agreement and other agreements as these agreements relate to the Partnership are
as follow:

    (a)  El Paso will acquire the minority interests of Leviathan Holdings and
         two other subsidiaries of DeepTech primarily held by DeepTech
         management for an aggregate of $55.0 million. As a result, El Paso will
         own 100% of Leviathan's general partner interest in the Partnership and
         an overall 27.3% effective interest in the Partnership.


                                       5
<PAGE>   8

             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)

    (b)  Pursuant to the Merger Agreement, employees of DeepTech or the
         Partnership who are terminated upon the closing of the Merger or during
         the six months thereafter, will receive certain severance payments from
         DeepTech or El Paso.

    (c)  Tatham Offshore, Inc. ("Tatham Offshore"), an affiliate of the
         Partnership, will transfer certain of its assets located in the Gulf to
         the Partnership in consideration of the redemption by Tatham Offshore
         of its 7,500 shares of Series B 9% Senior Convertible Preferred Stock
         (the "Senior Preferred Stock") currently owned by the Partnership (the
         "Redemption Agreement"). Specifically, under the terms of the
         Redemption Agreement and subject to the satisfaction of certain
         conditions at closing, the Partnership has agreed to exchange the
         Senior Preferred Stock and all related accrued and unpaid dividends due
         to the Partnership as of the date of the exchange for 100% of Tatham
         Offshore's right, title and interest in and to Viosca Knoll Blocks 772,
         773, 774, 817, 818 and 861 (subject to an existing production payment
         obligation), West Delta Block 35, Ewing Bank Blocks 871, 914, 915 and
         916 and the platform located at Ship Shoal Block 331. At the closing,
         the Partnership will receive from/pay to Tatham Offshore an amount
         equal to the net cash generated from/required by such properties from
         January 1, 1998 through the closing date. In addition, the Partnership
         has agreed to assume all abandonment and restoration obligations
         associated with the platform and leases. This transaction is expected
         to close on the later of July 1, 1998 or one business day after the
         closing of the rights offering related to DeepTech's merger with El
         Paso.

    (d)  Tatham Offshore has agreed to cancel its reversionary interests in
         certain oil and gas properties owned by the Partnership.

Both the Merger and the transactions contemplated by the Redemption Agreement
are subject to customary regulatory approvals, the satisfaction of certain
conditions and the consummation of certain related transactions and are
anticipated to be completed in June or July 1998.

Mr. Grant E. Sims and Mr. James H. Lytal, the Chief Executive Officer and the
President, respectively, of the Partnership have entered into employment
agreements with El Paso effective as of the closing of the Merger. After the
Merger, Messrs. Sims and Lytal will continue to serve as the Chief Executive
Officer and the President, respectively, of the Partnership for a term of five
years commencing on the effective date of the Merger. However, pursuant to the
terms of their respective employment agreements, Messrs. Sims and Lytal have the
right to terminate upon thirty days notice and El Paso has the right to
terminate under certain circumstances.


                                       6
<PAGE>   9
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)

NOTE 3 - EQUITY INVESTMENTS:

The Partnership owns interests of 50% in Viosca Knoll Gathering Company ("Viosca
Knoll"), 36% in Poseidon Oil Pipeline Company, L.L.C. ("POPCO"), 25.7% in
Nautilus Pipeline Company, L.L.C. ("Nautilus"), 25.7% in Manta Ray Offshore
Gathering Company, L.L.C. ("Manta Ray Offshore"), 50% in Stingray Pipeline
Company ("Stingray"), 40% in High Island Offshore System ("HIOS"), 33 1/3% in
U-T Offshore System ("UTOS") and 50% in West Cameron Dehydration Company, L.L.C.
("West Cameron Dehy"). The summarized financial information for these
investments, which are accounted for using the equity method, is as follows:


<TABLE>
<CAPTION>
                                             SUMMARIZED HISTORICAL OPERATING RESULTS
                                                         (In thousands)

                                                             Three Months Ended March 31, 1998
                            ----------------------------------------------------------------------------------------------------
                                                              West                                                               
                                      Viosca                 Cameron                             Manta Ray                       
                             HIOS     Knoll       Stingray    Dehy        POPCO         UTOS     Offshore       Nautilus    Total
<S>                       <C>         <C>          <C>         <C>        <C>          <C>         <C>         <C>          <C>
Operating revenue         $ 10,928    $ 7,027      $ 5,519     $ 565      $ 8,097      $1,091      $1,533      $   638           
Other income                    55         11          224         1           75          25         118           10           
Operating expenses          (4,047)      (651)      (3,439)      (46)        (888)       (601)       (305)        (253)          
Depreciation                (1,192)      (930)      (1,808)       (4)      (2,196)       (140)     (1,031)      (1,411)          
Other expenses                --         (929)        (305)       --       (2,198)         --          --          (12)          
                          --------    -------      -------     -----      -------      ------      ------      -------
Net earnings (loss)          5,744      4,528          191       516        2,890         375         315       (1,028)          
Ownership percentage            40%        50%          50%       50%          36%       33.3%       25.7%        25.7%          
                          --------    -------      -------     -----      -------      ------      ------      -------
                             2,298      2,264           96       258        1,040         125          81         (264)          
Adjustments:                                                                                                                     
- Depreciation(a)              190       --            234       --          --             8         (87)          --           
- Contract amortization(a)     (26)      --            (95)      --          --            --          --           --           
- Other                        (41)      --            (12)      --           (30)        (10)         --         (710)(c)       
                          --------    -------      -------     -----      -------      ------      ------      -------
Equity in earnings (loss) $  2,421    $ 2,264      $   223     $ 258      $ 1,010      $  123      $   (6)     $  (974)     $5,319
                          ========    =======      =======     =====      =======      ======      ======      =======      ======
Distributions(b)          $  2,400    $ 2,150      $ 1,000     $ 275      $  --        $   --      $  500      $    --      $6,325
                          ========    =======      =======     =====      =======      ======      ======      =======      ======
</TABLE>

------------
   (a) Adjustments result from purchase price adjustments made in accordance
       with Accounting Principles Board Opinion No. 16, "Business Combinations."
   (b) Future distributions could be restricted by the terms of the equity
       investees' respective credit agreements.
   (c) Primarily relates to a revision of the allowance for funds used during
       construction ("AFUDC") which represents the estimated costs, during the
       construction period, of funds used for construction purposes.



                                       7
<PAGE>   10
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)

                     SUMMARIZED HISTORICAL OPERATING RESULTS
                                 (In thousands)

<TABLE>
<CAPTION>                                                                                                                       
                                                              Three Months Ended March 31, 1997                                 
                                ------------------------------------------------------------------------------------------------
                                           Viosca                West Cameron                               Manta Ray              
                                HIOS        Knoll      Stingray      Dehy          POPCO        UTOS        Offshore       Total
<S>                          <C>          <C>          <C>         <C>            <C>         <C>            <C>        <C>     
Operating revenue            $ 11,679      $ 4,926      $  6,214    $  796         $ 4,131      $ 959        $ 1,103            
Other income                      114           --           233         7              44          8            110            
Operating expenses             (3,872)       (607)        (2,833)      (41)           (825)      (607)          (371)           
Depreciation                   (1,194)       (586)        (1,802)       (4)           (895)      (141)          (333)           
Other expenses                     --        (456)          (368)       --          (1,265)        --             --            
                             --------      ------       --------    ------         -------      -----         ------            
Net earnings                    6,727       3,277          1,444       758           1,190        219            509            
Ownership percentage               40%         50%            50%       50%             36%      33.3%          25.7%           
                             --------      ------       --------    ------         -------      -----         ------            
                                2,691       1,639            722       379             428         73            131            
Adjustments:                                                                                                                    
- Depreciation(a)                 211          --            238        --              --          9             --
- Contract amortization(a)        (26)         --            (85)       --              --         --             --
- Other                           (39)         --            (12)       --             109         (8)           629(b)
                             --------      ------       --------    ------         -------      -----         ------
Equity in earnings           $  2,837      $1,639       $    863    $  379         $   537      $  74         $  760        $7,089
                             ========      ======       ========    ======         =======      =====         ======        ======
Distributions(c)             $  3,200      $1,350       $    550    $  175         $    --      $  --         $   --        $5,275
                             ========      ======       ========    ======         =======      =====         ======        ======
</TABLE>

------------------
(a)  Adjustments result from purchase price adjustments made in accordance with
     Accounting Principles Board Opinion No. 16, "Business Combinations."
(b)  Represents additional net earnings specifically allocated to the
     Partnership related to the assets contributed by the Partnership to the
     Manta Ray Offshore joint venture. Pursuant to the terms of the joint
     venture agreement, the Partnership managed the operations of the assets
     contributed to Manta Ray Offshore and was permitted to retain approximately
     100% of the net earnings from such assets during the construction phase of
     the expansion to the Manta Ray Offshore system (January 17, 1997 through
     December 31, 1997). Effective January 1, 1998, Manta Ray Offshore began
     allocating all net earnings in accordance with the ownership percentages of
     the joint venture.
(c)  Future distributions could be restricted by the terms of the equity
     investees' respective credit agreements.

NOTE 4 - PARTNERS' CAPITAL INCLUDING CASH DISTRIBUTIONS:

Cash distributions

Distributions by the Partnership of its Available Cash are effectively made 98%
to Unitholders and 2% to Leviathan, subject to the payment of incentive
distributions to Leviathan if certain target levels of cash distributions to
Unitholders are achieved (the "Incentive Distributions"). As an incentive, the
general partner's interest in the portion of quarterly cash distributions in
excess of $0.325 per Unit and less than or equal to $0.375 per Unit is increased
to 15%. For quarterly cash distributions over $0.375 per Unit but less than or
equal to $0.425 per Unit, the general partner receives 25% of such incremental
amount and for all quarterly cash distributions in excess of $0.425 per Unit,
the general partner receives 50% of the incremental amount.

In February 1998, the Partnership paid a cash distribution of $0.50 per
Preference and Common Unit for the period from October 1, 1997 through December
31, 1997 and an Incentive Distribution of $2.4 million to Leviathan, as general
partner. On April 15, 1998, the Partnership declared a cash distribution of
$0.525 per Preference and Common Unit for the period from January 1, 1998
through March 31, 1998 which will be paid on May 15, 1998 to Unitholders of
record as of April 30, 1998. Leviathan will receive an Incentive Distribution of
$3.0 million for the three months ended March 31, 1998.

Conversion of Preference Units into Common Units

The Preference Units are currently entitled to receive from Available Cash, as
defined in the Partnership Agreement, a minimum quarterly distribution for each
quarter of $0.275 per Preference Unit, plus any arrearage in the payment of the
minimum quarterly distribution for prior quarters, before any distribution of
Available Cash is made to holders of Common Units for such quarter.



                                       8
<PAGE>   11
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)


In May 1998, the Partnership notified the holders of its Preference Units of
their right to convert their Preference Units into an equal number of Common
Units, provided that, on August 5, 1998, after giving effect to the conversion
of all Preference Units as to which a notice of conversion had been timely
received by the Partnership, there were at least 2,000 holders of 100 or more
Common Units of the Partnership (the "Liquidity Condition"). Subject to the
satisfaction of the Liquidity Condition, after August 5, 1998, Preference Units
will not be entitled to (i) any cash distributions in excess of the minimum
quarterly distribution of $0.275 per Unit or (ii) any distribution preferences
over the Common Units, and the preference period will end.

Subject to the satisfaction of the Liquidity Condition, holders of Preference
Units must convert to Common Units in order to participate in (i) any cash
distributions above the minimum quarterly distributions of $0.275 per Unit or
(ii) future increases of such distributions of the Partnership, if any. The
Partnership anticipates that substantially all of the holders of the Preference
Units will elect to convert their Preference Units into Common Units since the
current quarterly distributions are significantly in excess of the minimum
quarterly distribution; however, no assurance can be made that the current
quarterly distribution rate will be increased or maintained.

If less than all of the Preference Units are converted into Common Units as of
August 5, 1998, the Partnership must again notify the remaining holders of the
Preference Units of their right to convert their Preference Units into Common
Units once each year for another two years.

NOTE 5 - RELATED PARTY TRANSACTIONS:

Management fees. For the three months ended March 31, 1998, Leviathan charged
the Partnership $2.5 million pursuant to the Partnership Agreement which
provides for reimbursement of expenses Leviathan incurs as general partner of
the Partnership, including reimbursement of expenses incurred by DeepTech in
providing management services to Leviathan and the Partnership.

Other. Tatham Offshore Canada Limited ("Tatham Offshore Canada"), a wholly-owned
subsidiary of Tatham Offshore, is the Canadian representative of North Atlantic
Pipeline Partners, L.P. ("North Atlantic"), the sponsor of a proposal to build
an approximately 2,500 kilometer pipeline from offshore Newfoundland and Nova
Scotia to the eastern seaboard of the United States. The Partnership has entered
into a letter agreement with Tatham Offshore Canada regarding participation in
the North Atlantic pipeline project. Under such agreement, Tatham Offshore
Canada is responsible for the pre-development costs of the project. Such
agreement contains certain termination rights, contemplates the negotiation,
execution and delivery of definitive agreements and provides that the
Partnership would hold a pro rata partnership interest of up to 20% in North
Atlantic. The Partnership has no financial commitment to the project until and
unless an application is approved by the appropriate Canadian and United States
regulatory authorities. In the event the Partnership was to terminate its
participation in North Atlantic after the date North Atlantic receives
regulatory approval of an application but prior to the in-service date of the
first phase of the North Atlantic pipeline, the Partnership, under certain
conditions, would be obligated to pay Tatham Offshore Canada an amount equal to
150% of the Partnership's pro rata share of the "success fee" earned by Tatham
Offshore Canada related to the first phase of construction. For a period of one
year after the effective date of the merger discussed in Note 2, the Partnership
shall have the right to terminate this agreement without incurring the liability
for the above-mentioned "success fee". Tatham Offshore Canada is seeking
additional participants on the same basis as that offered to the Partnership.

Pursuant to the Leviathan non-employee director compensation arrangements, the
Partnership is obligated to pay each non-employee director 2 1/2% of the general
partner's Incentive Distribution as a profit participation fee. During the three
months ended March 31, 1998, the Partnership paid the three non-employee
directors of Leviathan a total of $0.2 million as a profit participation fee.

In March 1998, Tatham Offshore eliminated its 7,500 shares of 9% Senior
Convertible Preferred Stock issued to the Partnership and replaced this stock
with its Senior Preferred Stock (discussed in Note 2). The Partnership, at any
time, may convert the shares of Senior Preferred Stock into shares of Tatham



                                       9
<PAGE>   12
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)


Offshore Series A 12% Convertible Exchangeable Preferred Stock ("Series A
Preferred Stock") using a conversion ratio equal to (i) the liquidation
preference amount plus accumulated and unpaid dividends divided by (ii) $0.9375,
the closing price of the Tatham Offshore Series A Preferred Stock on February
27, 1998. In connection with the Redemption Agreement discussed in Note 2, the
Senior Preferred Stock and all related unpaid dividends will be redeemed in
full.

NOTE 6 - COMMITMENTS AND CONTINGENCIES:

Hedging Activities

The Partnership hedges a portion of its oil and natural gas production to reduce
the Partnership's exposure to fluctuations in market prices of oil and natural
gas and to meet certain requirements of the Partnership Credit Facility (as
defined herein). The Partnership uses various financial instruments whereby
monthly settlements are based on differences between the prices specified in the
instruments and the settlement prices of certain futures contracts quoted on the
New York Mercantile Exchange ("NYMEX") or certain other indices. The Partnership
settles the instruments by paying the negative difference or receiving the
positive difference between the applicable settlement price and the price
specified in the contract. The instruments utilized by the Partnership differ
from futures contracts in that there is no contractual obligation which requires
or allows for the future delivery of the product. Gains or losses on hedging
activities are recognized as oil and gas sales in the period in which the hedged
production is sold.

At March 31, 1998, the Partnership had open sales hedges on approximately 25,000
million British thermal units ("MMbtu") of natural gas per day for the remaining
period in 1998 at an average price of $2.37 per MMbtu and open purchase hedges
of approximately 25,000 MMbtu of natural gas per day for the remaining period in
1998 at an average price of $2.24 per MMbtu. In addition, the Partnership had
entered into commodity swap transactions for calendar 1999 totaling 5,000 MMbtu
per day at a fixed price to be determined at the Partnership's option equal to
the January 1999 Natural Gas Futures Contract on NYMEX as quoted at any time
during 1998 to and including the last three trading days of the January 1999
contract minus $0.25 per MMbtu.

At March 31, 1998, the Partnership had open sales hedges on approximately 990
barrels of oil per day for the remaining period in 1998 at an average price of
$20.43 per barrel and open purchase hedges of approximately 1,000 barrels of oil
per day for the remaining period in 1998 at an average price of $17.45 per
barrel.

Other

In 1995, the Partnership adopted the Unit Rights Appreciation Plan (the "Plan")
to provide the Partnership with the ability of making awards of Unit Rights, as
hereinafter defined, to certain officers and employees of the Partnership or its
affiliates as an incentive for these individuals to continue in the service of
the Partnership or its affiliates. Under the Plan, the Partnership has granted
to certain officers and employees of the Partnership or its affiliates the right
to purchase, or realize the appreciation of, a Preference Unit or Common Unit
(see Note 4) (a "Unit Right"), pursuant to the provisions of the Plan. As of
March 31, 1998, a total of 1,200,000 Unit Rights had been granted under the
Plan. The exercise prices of the Preference Units covered by the Unit Rights
granted pursuant to the Plan range from $15.6875 to $21.50, the closing prices
of the Preference Units as reported on the New York Stock Exchange on the date
the Unit Rights were granted. As of March 31, 1998, the Partnership had accrued
$5.7 million related to the appreciation and vesting of the outstanding Unit
Rights. However, as a result of the "change of control" occurring upon the
closing of the Merger discussed in Note 2, the Unit Rights will fully vest and
the Partnership will be obligated to pay the holders of the Unit Rights an
amount equal to the difference between the grant price of the Preference Units
and the closing price of the Preference Units on the date of the Merger, or a
date otherwise specified. The closing price of the Preference Units on May 11,
1998 was $29 15/16 per Unit.


                                       10
<PAGE>   13

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS 
OF OPERATIONS

The following discussion should be read in conjunction with the Partnership's
consolidated financial statements and notes thereto included in Item 1.
"Consolidated Financial Statements" and is intended to assist in the
understanding of the Partnership's financial condition and results of operations
for the three months ended March 31, 1998. Unless the context otherwise
requires, all references herein to the Partnership with respect to the
operations and ownership of the Partnership's assets are also references to its
subsidiaries.

OVERVIEW

The Partnership's assets include interests in (i) eight natural gas pipelines
(the "Gas Pipelines"), (ii) a crude oil pipeline system, (iii) five
strategically located multi-purpose platforms, (iv) three producing oil and gas
properties and (v) a dehydration facility.

The Gas Pipelines, strategically located offshore Louisiana and eastern Texas,
gather and transport natural gas for producers, marketers, pipelines and
end-users for a fee. The Gas Pipelines include approximately 1,167 miles of
pipeline with a throughput capacity of 6.5 billion cubic feet ("Bcf") of gas per
day. Each of the Gas Pipelines interconnects with one or more long line
transmission pipelines that provide access to multiple markets in the eastern
half of the United States. The Partnership's interest in the Gas Pipelines
consists of: a 100% interest in each of Manta Ray Gathering Company, L.L.C.
("Manta Ray"), Green Canyon Pipe Line Company, L.L.C. ("Green Canyon") and
Tarpon Transmission Company ("Tarpon"); a 50% partnership interest in each of
Stingray and Viosca Knoll; a 40% partnership interest in HIOS; a 33 1/3%
partnership interest in UTOS; and an effective 25.7% interest in each of Manta
Ray Offshore and Nautilus.

The Partnership owns a 36% interest in POPCO which owns and operates the
Poseidon Oil Pipeline ("Poseidon"). Poseidon, a major new sour crude oil
pipeline system built in response to an increased demand for additional sour
crude oil pipeline capacity in the central Gulf, consists of 297 miles of
16-inch to 24-inch pipeline with a capacity of approximately 400,000 barrels per
day and is currently delivering an average of approximately 75,000 barrels of
oil per day.

The Partnership operates and owns interests in five strategically located
multi-purpose platforms in the Gulf that have processing capabilities which
complement the Partnership's pipeline operations and play a key role in the
development of oil and gas reserves. The platforms are used to interconnect the
offshore pipeline network and to provide an efficient means to perform pipeline
maintenance and to operate compression, separation, processing and other
facilities. In addition, the multi-purpose platforms serve as landing sites for
deeper water production and as sites for the location of gas compression
facilities and drilling operations.

The Partnership owns an interest in and is operator of three producing leases in
the Gulf. The Viosca Knoll Block 817 wells (75% working interest currently owned
by the Partnership) are currently producing a gross aggregate average of
approximately 49 million cubic feet ("MMcf") of gas per day. Pursuant to the
Redemption Agreement, the Partnership has agreed to acquire the remaining 25%
working interest in Viosca Knoll Block 817. The Garden Banks Block 72 wells (50%
working interest owned by the Partnership) are currently producing a gross
aggregate average of approximately 1,965 barrels of oil and 8 MMcf of gas per
day. The Garden Banks Block 117 wells (50% working interest owned by the
Partnership) are currently producing a gross aggregate average of approximately
1,975 barrels of oil and 3.7 MMcf of gas per day.

The Partnership owns a 50% interest in West Cameron Dehy, which owns certain
dehydration facilities located at the northern terminus of the Stingray system,
onshore Louisiana.


                                       11
<PAGE>   14
RESULTS OF OPERATIONS

THREE MONTHS ENDED MARCH 31, 1998 COMPARED WITH THREE MONTHS ENDED MARCH 31, 
1997

Oil and gas sales totaled $9.1 million for the three months ended March 31, 1998
as compared with $18.1 million for the same period in 1997. The decrease is
attributable to decreased production from the Partnership's oil and gas
properties, substantially lower realized oil prices and the lack of acceptable
markets downstream of the Viosca Knoll system. During the three months ended
March 31, 1998, the Partnership produced and sold 2,789 MMcf of gas and 170,095
barrels of oil at average prices of $2.20 per thousand cubic feet ("Mcf") and
$17.26 per barrel, respectively. During the same period in 1997, the Partnership
produced and sold 6,191 MMcf of gas and 203,000 barrels of oil at average prices
of $2.15 per Mcf and $22.53 per barrel, respectively.

Revenue from gathering, transportation and platform services totaled $3.3
million for the three months ended March 31, 1998 as compared with $5.8 million
for the same period in 1997. The decrease of $2.5 million reflects decreases of
(i) $1.4 million related to the cessation of production from the only well
connected to the Ewing Bank system, (ii) $0.5 million from the Tarpon system
primarily related to (x) the deregulation of the Tarpon system in March 1997
allowing the Partnership to recognize additional revenue of $0.7 million during
the three months ended March 31, 1997 related to the gathering fees collected in
prior periods offset by (y) new production attached to the system, (iii) $0.4
million as a result of the contribution of a significant portion of the Manta
Ray system to Manta Ray Offshore on January 17, 1997 resulting in revenue from
these assets being included in equity in earnings for all of the three months in
the period ended March 31, 1998 as compared with a portion of the three months
ended March 31, 1997 and (iv) $0.2 million in platform services revenue from the
Partnership's Viosca Knoll Block 817 platform as a result of lower oil and gas
volumes processed on the platform. Gathering volumes from the Tarpon system
increased approximately 265% during the first quarter of 1998 as compared with
the first quarter of 1997 as a result of new producing fields attached to the
system in June and July 1997. Gathering volumes from the Ewing Bank system
declined 100% during the first quarter of 1998 as compared with the first
quarter of 1997 due to the cessation of oil and gas production from the one well
attached to the system in May 1997. Gathering volumes for the Green Canyon
system decreased approximately 2% for the three months ended March 31, 1998 as
compared with the same period in 1997.

Revenue from the Partnership's equity interests in Stingray, HIOS, UTOS, Viosca
Knoll, POPCO, Manta Ray Offshore, Nautilus and West Cameron Dehy (the "Equity
Investees") totaled $5.3 million for the three months ended March 31, 1998 as
compared with $7.1 million for the same period in 1997. The decrease of $1.8
million primarily reflects decreases of (i) $1.1 million related to Stingray and
HIOS as a result of increased maintenance costs and decreased throughput and
(ii) $1.8 million related to nonrecurring start-up costs, prior period
adjustments and a change in equity ownership of Nautilus and Manta Ray Offshore
offset by increases of (iii) $0.6 million from Viosca Knoll as a result of
increased throughput and (iv) $0.5 million from POPCO which placed a third phase
of Poseidon in service in December 1997. Total gas throughput volumes for the
Equity Investees increased approximately 10% from the three months ended March
31, 1997 to the three months ended March 31, 1998 primarily as a result of
increased throughput on the Viosca Knoll, Nautilus, Manta Ray Offshore and UTOS
systems. Oil volumes from Poseidon totaled 6.7 million barrels and 3.7 million
barrels for the three months ended March 31, 1998 and 1997, respectively.

Operating expenses for the three months ended March 31, 1998 totaled $2.8
million as compared to $3.1 million for the same period in 1997. The decrease is
primarily attributable to lower operating and transportation costs associated
with the Partnership's oil and gas properties during the three months ended
March 31, 1998.

Depreciation, depletion and amortization totaled $7.9 million for the three
months ended March 31, 1998 as compared with $13.9 million for the same period
in 1997. The decrease of $6.0 million reflects decreases of (i) $4.2 million in
depreciation and depletion on oil and gas wells and facilities located on the
Viosca Knoll Block 817, Garden Banks Block 72 and the Garden Banks Block 117 as
a result of decreased production from these leases and (ii) $1.8 million in
depreciation on pipelines, platforms and facilities as a result of the
Partnership fully depreciating its investment in the Ewing Bank and Ship Shoal
systems in June 1997.


                                       12
<PAGE>   15
General and administrative expenses, including the management fee allocated from
Leviathan, totaled $5.0 million for the three months ended March 31, 1998 as
compared with $2.5 million for the same period in 1997. The increase of $2.5
million reflects increases of (i) $0.7 million in management fees allocated by
Leviathan to the Partnership as a result of increased operational activities and
(ii) $1.8 million in direct general and administrative expenses of the
Partnership primarily related to the appreciation and vesting of unit
appreciation rights granted to certain officers and employees in 1995, 1996 and
1997. See Item 1. "Consolidated Financial Statements -- Notes to Consolidated
Financial Statements -- Note 6 -- Commitments and Contingencies -- Other."

Interest income and other totaled $0.1 million for the three months ended March
31, 1998 as compared with $0.7 million for the three months ended March 31,
1997.

Interest and other financing costs, net of capitalized interest, for the three
months ended March 31, 1998 totaled $3.7 million as compared with $3.1 million
for the same period in 1997. During the three months ended March 31, 1998 and
1997, the Partnership capitalized $0.5 million and $0.8 million, respectively,
of interest costs in connection with construction projects and drilling
activities in progress during such periods.

Net loss for the three months ended March 31, 1998 totaled $1.4 million, or
$0.05 per Unit, as compared with net income of $9.0 million, or $0.32 per Unit,
for the three months ended March 31, 1997 as a result of the items discussed
above.

LIQUIDITY AND CAPITAL RESOURCES

Sources of Cash. The Partnership intends to satisfy its capital requirements and
other working capital needs primarily from cash on hand, cash from operations
and borrowings under the Partnership Credit Facility (discussed below). Net cash
provided by operating activities for the three months ended March 31, 1998
totaled $13.2 million. At March 31, 1998, the Partnership had cash and cash
equivalents of $1.3 million.

Cash from operations is derived from (i) payments for gathering gas through the
Partnership's 100% owned pipelines, (ii) platform access and processing fees,
(iii) cash distributions from Equity Investees and (iv) the sale of oil and gas
attributable to the Partnership's interest in its producing properties. Oil and
gas properties are depleting assets and will produce reduced volumes of oil and
gas in the future unless additional wells are drilled or recompletions of
existing wells are successful. See "-- Overview" for current production rates
from these properties.

The Partnership's cash flows from operations will be affected by the ability of
each Equity Investee to make distributions. Distributions from such entities are
subject to the discretion of their respective management committees. Further,
each of Stingray, POPCO and Viosca Knoll is party to a credit agreement under
which it has outstanding obligations that may restrict the payments of
distributions to its owners. Distributions to the Partnership from Equity
Investees during the three months ended March 31, 1998 totaled $6.3 million.

The Partnership Credit Facility is a revolving credit facility providing for up
to $300 million of available credit subject to customary terms and conditions,
including certain debt incurrence limitations. Proceeds from the Partnership
Credit Facility are available to the Partnership for general partnership
purposes, including financing of capital expenditures, for working capital, and
subject to certain limitations, for paying distributions to the Unitholders. The
Partnership Credit Facility can also be utilized to issue letters of credit as
may be required from time to time; however, no letters of credit are currently
outstanding. The Partnership Credit Facility matures in December 1999; is
guaranteed by Leviathan and each of the Partnership's subsidiaries; and is
secured by the management agreement with Leviathan, substantially all of the
assets of the Partnership and Leviathan's 1% general partner interest in the
Partnership and approximate 1% interest in certain subsidiaries of the
Partnership. As of March 31, 1998, the Partnership had $251.0 million
outstanding under its credit facility bearing interest at an average floating
rate of 6.3% per annum. In April 1998, the Partnership Credit Facility was
amended to allow for the Merger of DeepTech and El Paso, the acquisition of
certain assets from Tatham Offshore pursuant to the Redemption Agreement and
certain other transactions. Currently, approximately $32.0 million of
additional funds are available under the Partnership Credit Facility.


                                       13
<PAGE>   16
In March 1998, Stingray amended an existing term loan agreement to provide for
additional borrowings of $11.1 million and to extend the maturity date of the
loan from December 31, 2000 to March 31, 2003. The amended agreement requires
Stingray to make 18 quarterly principal payments of $1.6 million commencing on
December 31, 1998. The term loan agreement is principally secured by current and
future gas transportation contracts between Stingray and its customers. As of
March 31, 1998, Stingray had $28.5 million outstanding under its term loan
agreement bearing interest at an average floating rate of 6.5% per annum.

In April 1996, POPCO entered into a revolving credit facility (the "POPCO Credit
Facility") with a group of commercial banks to provide up to $150 million for
the construction and expansion of Poseidon and for other working capital needs
of POPCO. POPCO's ability to borrow money under the facility is subject to
certain customary terms and conditions, including borrowing base limitations.
The POPCO Credit Facility is secured by a substantial portion of POPCO's assets
and matures on April 30, 2001. As of March 31, 1998, POPCO had $123.0 million
outstanding under its credit facility bearing interest at an average floating
rate of 6.9% per annum. Currently, approximately $27.0 million of additional
funds are available under the POPCO Credit Facility.

In December 1996, Viosca Knoll entered into a revolving credit facility (the
"Viosca Knoll Credit Facility") with a syndicate of commercial banks to provide
up to $100 million for the addition of compression to the Viosca Knoll system
and for other working capital needs of Viosca Knoll, including funds for a
one-time distribution of $25 million to its partners. Viosca Knoll's ability to
borrow money under the facility is subject to certain customary terms and
conditions, including borrowing base limitations. The Viosca Knoll Credit
Facility is secured by a substantial portion of Viosca Knoll's assets and
matures on December 20, 2001. As of March 31, 1998, Viosca Knoll had $60.0
million outstanding under its credit facility bearing interest at an average
floating rate of 6.4% per annum. Currently, approximately $22.9 million of
additional funds are available under the Viosca Knoll Credit Facility.

Uses of Cash. The Partnership's capital requirements consist primarily of (i)
quarterly distributions to holders of Preference Units and Common Units and to
Leviathan as general partner, including Incentive Distributions, as applicable,
(ii) expenditures for the maintenance of its pipelines and related
infrastructure and the acquisition and construction of additional pipelines and
related facilities for the gathering, transportation and processing of oil and
gas in the Gulf, (iii) expenditures related to its producing oil and gas
properties, (iv) management fees and other operating expenses, (v) contributions
to Equity Investees as required to fund capital expenditures for new facilities,
(vi) debt service on its outstanding indebtedness and (vii) the payment of the
appreciation of Unit Rights as discussed in Item 1. "Consolidated Financial
Statements -- Notes to Consolidated Financial Statements -- Note 6 --
Commitments and Contingencies -- Other."

For every full quarter since its inception, the Partnership has declared and
subsequently paid a cash distribution to holders of Preference Units and Common
Units an amount equal to or exceeding the Minimum Quarterly Distribution (as
described in the Partnership Agreement) per Unit per quarter. See Item 1.
"Consolidated Financial Statements -- Notes to Consolidated Financial Statements
-- Note 4 -- Partners' Capital including Cash Distributions -- Conversion of
Preference Units into Common Units." At the current distribution rate of $0.525
per Unit, the quarterly Partnership distributions total $16.0 million in respect
of the Preference Units, Common Units and general partner interest ($64.0
million on an annual basis, including $26.1 million to Leviathan). The
Partnership believes that it will be able to continue to pay at least the
current quarterly distribution of $0.525 per Preference and Common Unit for the
foreseeable future.

Distributions by the Partnership of its Available Cash are effectively made 98%
to Unitholders and 2% to Leviathan, as general partner, subject to the payment
of Incentive Distributions to Leviathan. As an incentive, the general partner's
interest in the portion of quarterly cash distributions in excess of $0.325 per
Unit and less than or equal to $0.375 per Unit is increased to 15%. For
quarterly cash distributions over $0.375 per Unit but less than or equal to
$0.425 per Unit, the general partner receives 25% of such incremental amount and
for all quarterly cash distributions in excess of $0.425 per Unit, the general
partner receives 50% of the incremental amount. For the three months ended March
31, 1998, the Partnership paid Leviathan Incentive Distributions totaling $2.4
million and will pay Leviathan an Incentive Distribution of $3.0 million in May
1998.

The Partnership anticipates that its capital expenditures and equity investments
for the remaining portion of 1998 will relate to continuing acquisition and
construction activities including the construction and installation of a new


                                       14
<PAGE>   17
platform and processing facilities at East Cameron Block 373. This platform,
which the Partnership placed in service in April 1998 at a cost of approximately
$32 million, is strategically located to exploit reserves in the East Cameron
and Garden Banks area of the Gulf and is the terminus for an extension of the
Stingray system. The Partnership anticipates funding such cash requirements
primarily with available cash flow and borrowings under the Partnership Credit
Facility.

Any substantial capital expenditures by Stingray, POPCO and Viosca Knoll are
anticipated to be funded by borrowings under their respective credit facilities.
The Partnership's cash capital expenditures and equity investments for the three
months ended March 31, 1998 were $16.6 million. The Partnership may in the
future contribute existing assets to new joint ventures as partial consideration
for its ownership interest therein.

Interest costs incurred by the Partnership related to the Partnership Credit
Facility totaled $4.2 million for the three months ended March 31, 1998. The
Partnership capitalized $0.5 million of such interest costs in connection with
construction projects in progress during the period.

UNCERTAINTY OF FORWARD LOOKING STATEMENTS AND INFORMATION

This quarterly report contains certain forward looking statements and
information that are based on management's beliefs as well as assumptions made
by and information currently available to management. Such statements are
typically punctuated by words or phrases such as "anticipate," "estimate,"
"project," "should," "may," "management believes," and words or phrases of
similar import. Although management believes that such statements and
expressions are reasonable and made in good faith, it can give no assurance that
such expectations will prove to have been correct. Such statements are subject
to certain risks, uncertainties and assumptions. Should one or more of these
risks or uncertainties materialize, or should underlying assumptions prove
incorrect, actual results may vary materially from those anticipated, estimated
or projected. Among the key factors that may have a direct bearing on the
Partnership's results of operations and financial condition are: (i) competitive
practices in the industry in which the Partnership competes, (ii) the impact of
current and future laws and government regulations affecting the industry in
general and the Partnership's operations in particular, (iii) environmental
liabilities to which the Partnership may become subject in the future that are
not covered by an indemnity or insurance, (iv) the throughput levels achieved by
the Gas Pipelines, Poseidon and any future pipelines in which the Partnership
owns an interest, (v) the ability to access additional reserves to offset the
natural decline in production from existing wells connected to the Gas Pipelines
and Poseidon, (vi) changes in gathering, transportation, processing, handling
and other rates due to changes in governmental regulation and/or competitive
factors, (vii) the impact of oil and natural gas price fluctuations, (viii) the
production rates and reserve estimates associated with the Partnership's
producing oil and gas properties, (ix) significant changes from expectations of
capital expenditures and operating expenses and unanticipated project delays and
(x) the ability of the Equity Investees to make distributions to the
Partnership. The Partnership disclaims any obligation to update any
forward-looking statements to reflect events or circumstances after the date
hereof.


                                       15
<PAGE>   18

                           PART II. OTHER INFORMATION


ITEM 1.  LEGAL PROCEEDINGS

         None.

ITEM 2.  CHANGES IN SECURITIES AND USE OF PROCEEDS

         None.

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES

         None.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

         None.

ITEM 5.  OTHER INFORMATION

         None.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a)    Exhibits

                10.1  First Amendment to Second Amended and Restated Credit
                      Agreement dated December 13, 1996 among the Partnership,
                      Several Lenders, The Chase Manhattan Bank, as
                      Administrative Agent, and ING (U.S.) Capital Corporation,
                      as Co-Arranger.

                10.2  Second Amendment to Second Amended and Restated Credit
                      Agreement dated December 13, 1996 among the Partnership,
                      Several Lenders, The Chase Manhattan Bank, as
                      Administrative Agent, and ING (U.S.) Capital Corporation,
                      as Co-Arranger.

                10.3  Redemption Agreement dated February 27, 1998 between
                      Tatham Offshore, Inc. and Flextrend Development Company,
                      L.L.C.

                27    Financial Data Schedule

         (b)    Reports on Form 8-K

                None.


                                       16
<PAGE>   19
                                   SIGNATURES



    Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned and thereunto duly authorized.

    LEVIATHAN GAS PIPELINE
    PARTNERS, L.P.
    (Registrant)

    By:                          LEVIATHAN GAS PIPELINE
                                 COMPANY, its General Partner



    Date:  May 14, 1998          By: /s/ KEITH B. FORMAN
                                     --------------------------------
                                 Keith B. Forman
                                 Chief Financial Officer



    Date: May 14, 1998           By: /s/ DENNIS A. KUNETKA
                                     --------------------------------
                                 Dennis A. Kunetka
                                 Senior Vice President - Corporate Finance
                                 (Principal Accounting Officer)



                                       17
<PAGE>   20

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                        DESCRIPTION
-------                       -----------
<S>   <C>
10.1  First Amendment to Second Amended and Restated Credit Agreement dated
      December 13, 1996 among the Partnership, Several Lenders, The Chase
      Manhattan Bank, as Administrative Agent, and ING (U.S.) Capital
      Corporation, as Co-Arranger.

10.2  Second Amendment to Second Amended and Restated Credit Agreement dated
      December 13, 1996 among the Partnership, Several Lenders, The Chase
      Manhattan Bank, as Administrative Agent, and ING (U.S.) Capital
      Corporation, as Co-Arranger.

10.3  Redemption Agreement dated February 27, 1998 between Tatham Offshore, Inc.
      and Flextrend Development Company, L.L.C.

27    Financial Data Schedule
</TABLE>