<PAGE>   1
 
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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
 
                             ---------------------
 
                                   FORM 10-Q
 
(MARK ONE)
 
     [X]        QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
 
                 FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1999
 
                                       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)
 
<TABLE>
<S>                                             <C>
                  DELAWARE                                       76-0396023
        (State or Other Jurisdiction                          (I.R.S. Employer
      of Incorporation or Organization)                      Identification No.)
</TABLE>
 
<TABLE>
<S>                                            <C>
           EL PASO ENERGY BUILDING
            1001 LOUISIANA STREET
               HOUSTON, TEXAS                                      77002
  (Address of Principal Executive Offices)                      (Zip Code)
</TABLE>
 
       Registrant's Telephone Number, Including Area Code: (713) 420-2131
 
     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 12 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 [ ]
 
     The registrant had 23,349,988 Common Units and 1,016,906 Preference Units
outstanding at May 10, 1999.
 
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<PAGE>   2
 
                        PART I -- FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS
 
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
                  CONDENSED CONSOLIDATED STATEMENTS OF INCOME
                    (IN THOUSANDS, EXCEPT PER UNIT AMOUNTS)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                FIRST QUARTER
                                                               ENDED MARCH 31,
                                                              -----------------
                                                               1999      1998
                                                              -------   -------
<S>                                                           <C>       <C>
Revenue
  Oil and natural gas sales.................................  $ 6,805   $ 9,135
  Gathering, transportation and platform services...........    4,373     3,260
  Equity in earnings........................................   10,701     5,319
                                                              -------   -------
                                                               21,879    17,714
                                                              -------   -------
Costs and expenses
  Operating expenses........................................    2,594     2,837
  Depreciation, depletion and amortization..................    6,719     7,867
  General and administrative expenses and management fee....    3,130     4,950
                                                              -------   -------
                                                               12,443    15,654
                                                              -------   -------
Operating income............................................    9,436     2,060
Interest income and other...................................      103        84
Interest and other financing costs..........................   (6,102)   (3,722)
Minority interest in (income) loss..........................      (37)       13
                                                              -------   -------
Income (loss) before income taxes...........................    3,400    (1,565)
Income tax benefit..........................................       99       141
                                                              -------   -------
Net income (loss)...........................................  $ 3,499   $(1,424)
                                                              =======   =======
Weighted average number of units outstanding................   24,367    24,367
                                                              =======   =======
Basic and diluted net income (loss) per unit (Note 8).......  $  0.12   $ (0.05)
                                                              =======   =======
</TABLE>
 
  The accompanying Notes are an integral part of these Condensed Consolidated
                             Financial Statements.
 
                                        1
<PAGE>   3
 
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
                     CONDENSED CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                               MARCH 31,    DECEMBER 31,
                                                                 1999           1998
                                                              -----------   ------------
                                                              (UNAUDITED)
<S>                                                           <C>           <C>
Current assets
  Cash and cash equivalents.................................   $  6,371       $  3,108
  Accounts receivable.......................................      4,494          8,588
  Other current assets......................................        169            247
                                                               --------       --------
          Total current assets..............................     11,034         11,943
                                                               --------       --------
Equity investments..........................................    187,563        186,079
                                                               --------       --------
Property and equipment
  Pipelines.................................................     66,844         64,464
  Platforms and facilities..................................    124,387        123,912
  Oil and natural gas properties, at cost, using successful
     efforts method.........................................    155,514        152,750
                                                               --------       --------
                                                                346,745        341,126
  Less accumulated depreciation, depletion, amortization and
     impairment.............................................    106,175         99,134
                                                               --------       --------
     Property and equipment, net............................    240,570        241,992
                                                               --------       --------
Other noncurrent assets.....................................      4,073          2,712
                                                               --------       --------
          Total assets......................................   $443,240       $442,726
                                                               ========       ========
 
LIABILITIES AND PARTNERS' CAPITAL
 
Current liabilities
  Accounts payable and accrued liabilities..................   $  7,125       $ 11,167
  Notes payable.............................................    355,000        338,000
                                                               --------       --------
          Total current liabilities.........................    362,125        349,167
Other noncurrent liabilities................................     11,309         11,661
                                                               --------       --------
          Total liabilities.................................    373,434        360,828
Minority interest...........................................     (1,118)          (998)
Partners' capital...........................................     70,924         82,896
                                                               --------       --------
          Total liabilities and partners' capital...........   $443,240       $442,726
                                                               ========       ========
</TABLE>
 
  The accompanying Notes are an integral part of these Condensed Consolidated
                             Financial Statements.
 
                                        2
<PAGE>   4
 
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                 FIRST QUARTER
                                                                ENDED MARCH 31,
                                                              -------------------
                                                                1999       1998
                                                              --------   --------
<S>                                                           <C>        <C>
Cash flows from operating activities
  Net income (loss).........................................  $  3,499   $ (1,424)
  Adjustments to reconcile net income (loss) to net cash
     provided by operating activities
     Depreciation, depletion and amortization...............     6,719      7,867
     Distributed (undistributed) earnings in equity
      investees.............................................      (611)     1,006
     Other noncash items....................................       279      1,651
  Working capital changes...................................       130      4,099
                                                              --------   --------
          Net cash provided by operating activities.........    10,016     13,199
                                                              --------   --------
Cash flows from investing activities
  Additions to pipelines, platforms and facilities..........    (2,855)   (13,190)
  Investments in equity investees...........................      (873)    (3,338)
  Development of oil and natural gas properties.............    (2,764)       (43)
  Other.....................................................      (365)        --
                                                              --------   --------
          Net cash used in investing activities.............    (6,857)   (16,571)
                                                              --------   --------
Cash flows from financing activities
  Proceeds from notes payable...............................    22,000     23,000
  Repayments of notes payable...............................    (5,000)   (10,000)
  Debt issuance costs.......................................    (1,268)        --
  Distributions to partners.................................   (15,628)   (14,794)
                                                              --------   --------
          Net cash provided by (used in) financing
           activities.......................................       104     (1,794)
                                                              --------   --------
Increase (decrease) in cash and cash equivalents............     3,263     (5,166)
Cash and cash equivalents
  Beginning of period.......................................     3,108      6,430
                                                              --------   --------
  End of period.............................................  $  6,371   $  1,264
                                                              ========   ========
</TABLE>
 
  The accompanying Notes are an integral part of these Condensed Consolidated
                             Financial Statements.
 
                                        3
<PAGE>   5
 
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
             CONDENSED CONSOLIDATED STATEMENT OF PARTNERS' CAPITAL
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                   PREFERENCE   PREFERENCE    COMMON     COMMON       GENERAL
                                     UNITS      UNITHOLDERS   UNITS    UNITHOLDERS   PARTNER(A)      TOTAL
                                   ----------   -----------   ------   -----------   ----------     --------
<S>                                <C>          <C>           <C>      <C>           <C>            <C>
Partners' capital at December 31,
  1998...........................    1,017        $7,351      23,350    $ 90,972      $(15,427)     $ 82,896
Net income for the quarter ended
  March 31, 1999 (unaudited).....       --            63         --        2,773           663         3,499
Cash distributions (unaudited)...       --          (280)        --      (12,258)       (2,933)      (15,471)
                                     -----        ------      ------    --------      --------      --------
Partners' capital at March 31,
  1999 (unaudited)...............    1,017        $7,134      23,350    $ 81,487      $(17,697)(b)  $ 70,924
                                     =====        ======      ======    ========      ========      ========
</TABLE>
 
---------------
 
(a)  Leviathan Gas Pipeline Company, an indirect subsidiary of El Paso Energy
     Corporation, owns a 1% general partner interest in Leviathan Gas Pipeline
     Partners, L.P. ("Leviathan").
 
(b)  Pursuant to the terms of Leviathan's partnership agreement, no partner
     shall have any obligation to restore any negative balance in its capital
     account upon liquidation of Leviathan. Therefore, any net gains from the
     dissolution of Leviathan's assets would be allocated first to any
     then-outstanding deficit capital account balance before any of the
     remaining net proceeds would be distributed to the partners in accordance
     with their ownership percentages.
 
  The accompanying Notes are an integral part of these Condensed Consolidated
                             Financial Statements.
 
                                        4
<PAGE>   6
 
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                  (UNAUDITED)
 
NOTE 1 -- ORGANIZATION AND BASIS OF PRESENTATION:
 
     Leviathan Gas Pipeline Partners, L.P. ("Leviathan"), a publicly held
Delaware master limited partnership, is a provider of integrated energy
services, including natural gas and oil gathering, transportation, midstream and
other related services in the Gulf of Mexico (the "Gulf"). Through its
subsidiaries and joint ventures, Leviathan owns interests in significant assets,
including (i) eight existing natural gas pipelines (the "Gas Pipelines"), (ii) a
crude oil pipeline system, (iii) six strategically-located multi-purpose
platforms, (iv) production handling and dehydration facilities, (v) four
producing oil and natural gas properties and (vi) a non-producing oil and
natural gas property, the Ewing Bank 958 Unit, comprised of Ewing Bank Blocks
958, 959, 1002 and 1003, formerly referred to as the Sunday Silence property.
 
     Leviathan Gas Pipeline Company ("General Partner"), a Delaware corporation
and wholly owned indirect subsidiary of El Paso Energy Corporation ("El Paso
Energy"), is the general partner of Leviathan, and as such, performs all
management and operational functions for Leviathan and its subsidiaries.
 
     As of March 31, 1999, Leviathan had 23,349,988 Common Units and 1,016,906
Preference Units outstanding. Preference Units and Common Units totaling
18,075,000 are owned by the public, representing a 72.7% effective limited
partner interest in Leviathan. The General Partner, through its ownership of a
25.3% limited partner interest in the form of 6,291,894 Common Units, its 1%
general partner interest in Leviathan and its approximate 1% nonmanaging
interest in certain subsidiaries of Leviathan, owns a 27.3% effective interest
in Leviathan. See Note 5.
 
     The 1998 Annual Report on Form 10-K for Leviathan includes a summary of
significant accounting polices and other disclosures and should be read in
conjunction with this Form 10-Q. The condensed consolidated financial statements
at March 31, 1999, and for the quarters ended March 31, 1999, and 1998, are
unaudited. The condensed balance sheet at December 31, 1998, is derived from
audited financial statements. These financial statements do not include all
disclosures required by generally accepted accounting principles, but have been
prepared pursuant to the rules and regulations of the U.S. Securities and
Exchange Commission. In the opinion of management, all material adjustments
necessary to present fairly the consolidated financial position and results of
operations for such periods have been included. All such adjustments are of a
normal recurring nature. Results of operations for any interim period are not
necessarily indicative of the results of operations for the entire year due to
the seasonal nature of Leviathan's businesses.
 
NOTE 2 -- EQUITY INVESTMENTS:
 
     Leviathan owns interests of 50% in Viosca Knoll Gathering Company ("Viosca
Knoll"), 36% in Poseidon Oil Pipeline Company, L.L.C. ("POPCO"), 50% in Stingray
Pipeline Company ("Stingray"), an indirect 40% in each of High Island Offshore
System, L.L.C. ("HIOS") and in East Breaks Gathering Company, L.L.C. ("East
Breaks"), 33.3% in U-T Offshore System ("UTOS"), 50% in West Cameron Dehydration
Company, L.L.C. ("West Cameron Dehy") and an indirect 25.67% interest in each of
Manta Ray Offshore Gathering Company, L.L.C. ("Manta Ray Offshore") and Nautilus
Pipeline Company, L.L.C. ("Nautilus") (collectively, the "Equity Investees").
The summarized financial information for these investments, which are accounted
for using the equity method, is as follows:
 
                                        5
<PAGE>   7
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
                    SUMMARIZED HISTORICAL OPERATING RESULTS
                          QUARTER ENDED MARCH 31, 1999
                                 (IN THOUSANDS)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                               WEST
                                      VIOSCA                  CAMERON                      MANTA RAY
                            HIOS(A)    KNOLL       STINGRAY    DEHY      POPCO    UTOS    OFFSHORE(B)   NAUTILUS(B)    TOTAL
                            -------   -------      --------   -------   -------   -----   -----------   -----------   -------
<S>                         <C>       <C>          <C>        <C>       <C>       <C>     <C>           <C>           <C>
Operating revenue.........  $10,006   $ 7,361      $ 4,432     $831     $16,778   $993      $ 3,446       $ 2,051
Other income..............      58         16          600        6        118      19          764          (234)
Operating expenses........  (3,858)      (270)      (3,158)     (75)    (1,671)   (452)      (1,040)         (501)
Depreciation..............  (1,091)      (950)      (1,901)      (4)    (1,911)   (140)      (1,221)       (1,479)
Interest expense..........      --     (1,125)          --       (8)    (2,116)     --           --            --
                            -------   -------      -------     ----     -------   -----     -------       -------
Net earnings (loss).......   5,115      5,032          (27)     750     11,198     420        1,949          (163)
Ownership percentage......      40%        50%(c)       50%      50%        36%   33.3%       25.67%        25.67%
                            -------   -------      -------     ----     -------   -----     -------       -------
                             2,046      2,516          (14)     375      4,031     140          500           (42)
Adjustments:
  Depreciation(d).........     179         --          213       --        (30)      9          (87)           --
  Contract
    amortization(d).......     (26)        --           --       --         --      --           --            --
  Other...................      32         --          899(e)    --         --      18           --           (58)
                            -------   -------      -------     ----     -------   -----     -------       -------
Equity in earnings
  (loss)..................  $2,231    $ 2,516      $ 1,098     $375     $4,001    $167      $   413       $  (100)    $10,701
                            =======   =======      =======     ====     =======   =====     =======       =======     =======
Distributions(f)..........  $1,600    $ 3,350      $    --     $275     $2,639    $333      $ 1,366       $   527     $10,090
                            =======   =======      =======     ====     =======   =====     =======       =======     =======
</TABLE>
 
---------------
 
(a)  As a result of restructuring the joint venture arrangement in December
     1998, the partners of the High Island Offshore System, a Delaware
     partnership, (i) created a holding company, Western Gulf Holdings, L.L.C.
     ("Western Gulf"), (ii) converted the Delaware partnership into a limited
     liability company and (iii) formed East Breaks. Western Gulf owns 100% of
     each of HIOS and East Breaks. HIOS owns a regulated natural gas system, and
     East Breaks is currently constructing an unregulated natural gas system.
     Leviathan believes the disclosure of separate financial data for HIOS and
     East Breaks is more meaningful than the consolidated results of Western
     Gulf, however, East Breaks only had construction activity during the
     period.
 
(b)  Leviathan owns a 25.67% interest in Neptune Pipeline Company, L.L.C.
     ("Neptune"). Neptune owns a 99% member interest in each of Manta Ray
     Offshore, which owns an unregulated natural gas system, and Nautilus, which
     owns a regulated natural gas system. Leviathan believes the disclosure of
     separate financial data for Manta Ray Offshore and Nautilus is more
     meaningful than the consolidated results of Neptune.
 
(c)  Leviathan has entered into an agreement to acquire an additional 49%
     interest in Viosca Knoll from El Paso Energy, and has an option to purchase
     the remaining 1% interest. See Note 5 for a further description of such
     agreement.
 
(d)  Adjustments result from purchase price adjustments made in accordance with
     Accounting Principles Board Opinion No. 16, "Business Combinations."
 
(e)  Adjustments resulting from changes in prior period estimates of reserves
     for uncollectible revenues.
 
(f)  Future distributions are at the discretion of Equity Investees' management
     committees and could further be restricted by the terms the Equity
     Investees' respective credit agreements.
 
                                        6
<PAGE>   8
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
                    SUMMARIZED HISTORICAL OPERATING RESULTS
                          QUARTER ENDED MARCH 31, 1998
                                 (IN THOUSANDS)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                              WEST
                                         VIOSCA              CAMERON                       MANTA RAY
                                HIOS     KNOLL    STINGRAY    DEHY      POPCO     UTOS    OFFSHORE(A)   NAUTILUS(A)   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)
Interest expense.............       --    (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%       25.67%        25.67%
                               -------   ------   -------     ----     -------   ------     -------       -------
                                 2,298   2,264         96      258      1,040      125           81          (264)
Adjustments:
  Depreciation(b)............      190      --        234       --        (30)       8          (87)           --
  Contract amortization(b)...      (26)     --        (95)      --         --       --           --            --
  Other......................      (41)     --        (12)      --         --      (10)          --          (710)(c)
                               -------   ------   -------     ----     -------   ------     -------       -------
Equity in earnings (loss)....  $ 2,421   $2,264   $   223     $258     $1,010    $ 123      $    (6)      $  (974)    $5,319
                               =======   ======   =======     ====     =======   ======     =======       =======     ======
Distributions................  $ 2,400   $2,150   $ 1,000     $275     $   --    $  --      $   500       $    --     $6,325
                               =======   ======   =======     ====     =======   ======     =======       =======     ======
</TABLE>
 
---------------
 
(a)  Leviathan owns a 25.67% interest in Neptune. Neptune owns a 99% member
     interest in each of Manta Ray Offshore, which owns an unregulated natural
     gas system, and Nautilus, which owns a regulated natural gas system.
     Leviathan believes the disclosure of separate financial data for Manta Ray
     Offshore and Nautilus is more meaningful than the consolidated results of
     Neptune.
 
(b)  Adjustments result from purchase price adjustments made in accordance with
     Accounting Principles Board Opinion No. 16, "Business Combinations."
 
(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.
 
NOTE 3 -- BUSINESS SEGMENT INFORMATION:
 
     Leviathan's operations consist of three segments: (i) gathering,
transportation, and platform services, (ii) oil and natural gas and (iii) equity
investments. All of Leviathan's operations are conducted in the Gulf. The
gathering, transportation, and platform services segment owns interests in
natural gas systems and platforms strategically located offshore Texas,
Louisiana, and Mississippi that provide services to producers, marketers, other
pipelines and end-users for a fee. Leviathan is engaged in the development and
production of hydrocarbons through its oil and natural gas segment. Equity
investments primarily include Leviathan's nonregulated and regulated gathering
and transportation activities that are conducted through joint ventures,
organized as general partnerships or limited liability companies, with
subsidiaries of major energy companies. The operational and administrative
activities of Leviathan's equity investments are primarily conducted by the
major energy companies and management decisions related to the operations are
made by management committees comprised of representatives of each partner or
member, as applicable, with authority appointed in direct relationship to
ownership interests (Note 2). Leviathan evaluates segment performance based on
net cash flows which consists of operating income (loss) plus depletion,
depreciation, abandonment, and impairment included in determining operating
income (loss) and, for equity investees, cash distributions. The
 
                                        7
<PAGE>   9
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
accounting policies of the individual segments are the same as those of
Leviathan. The following table summarizes certain financial information for each
business segment (in thousands):
 
<TABLE>
<CAPTION>
                                 GATHERING,
                               TRANSPORTATION
                                AND PLATFORM      OIL AND       EQUITY                 ELIMINATIONS
                                  SERVICES      NATURAL GAS   INVESTMENTS   SUBTOTAL    AND OTHER      TOTAL
                               --------------   -----------   -----------   --------   ------------   --------
<S>                            <C>              <C>           <C>           <C>        <C>            <C>
QUARTER ENDED MARCH 31, 1999:
  Revenue from external
     customers...............     $  4,373        $ 6,805      $ 10,701     $ 21,879     $    --      $ 21,879
  Intersegment revenue.......        2,874             --            --        2,874      (2,874)           --
  Depreciation, depletion and
     amortization............       (1,920)        (4,799)           --       (6,719)         --        (6,719)
  Operating income (loss)....        2,943         (2,866)        9,359        9,436          --         9,436
  Net cash flows.............        4,863          1,933         8,748       15,544          --        15,544
  Segment assets.............      156,199         88,360       188,065      432,624      10,616       443,240
QUARTER ENDED MARCH 31, 1998:
  Revenue from external
     customers...............     $  3,260        $ 9,135      $  5,319     $ 17,714     $    --      $ 17,714
  Intersegment revenue.......        2,589             --            --        2,589      (2,589)           --
  Depreciation, depletion and
     amortization............       (1,616)        (6,251)           --       (7,867)         --        (7,867)
  Operating income (loss)....          429         (2,048)        3,679        2,060          --         2,060
  Net cash flows.............        2,045          4,203         4,685       10,933          --        10,933
  Segment assets.............      145,336         64,915       186,601      396,852      13,948       410,800
</TABLE>
 
NOTE 4 -- PARTNERS' CAPITAL INCLUDING CASH DISTRIBUTIONS:
 
  Cash distributions
 
     In February 1999, Leviathan paid a cash distribution of $0.275 per
Preference Unit and $0.525 per Common Unit for the period from October 1, 1998
through December 31, 1998 and an incentive distribution of $2.8 million to the
General Partner. On April 20, 1999, Leviathan declared a cash distribution of
$0.275 per Preference Unit and $0.525 per Common Unit for the period from
January 1, 1999, through March 31, 1999, which was paid on May 14, 1999 to all
holders of record of Common Units and Preference Units as of April 30, 1999. The
General Partner received an incentive distribution of $2.8 million for the
quarter ended March 31, 1999. At the current distribution rates, the General
Partner receives approximately 19% of total cash distributions paid by Leviathan
and is thus allocated approximately 19% of Leviathan's net income.
 
  Conversion of Preference Units into Common Units
 
     On May 14, 1999, Leviathan notified the holders of its 1,016,906
outstanding Preference Units of their opportunity to submit their Preference
Units for conversion into an equal number of Common Units during a 90-day
period. The conversion period will expire on August 12, 1999. Remaining
Preference Units, if any, will retain their distribution preferences over the
Common Units; that is, no Common Unitholder or the General Partner will receive
any quarterly distribution until each Preference Unitholder has received the
minimum quarterly distribution of $0.275 per unit plus any arrearages. Holders
of the Common Units and the General Partner, however, are entitled to
distributions in excess of $0.275 per unit. Preference Units are not entitled to
any such excess distributions. Further, after the conversion period expires, any
remaining preference units may be subject to delisting by the New York Stock
Exchange ("NYSE") and, in certain circumstances, any remaining Preference Units
may be subject to mandatory redemption at a price below the market trading
price.
 
                                        8
<PAGE>   10
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     In accordance with Leviathan's partnership agreement, holders of Preference
Units not converting to Common Units during this 90-day period will have another
opportunity to convert their Preference Units into Common Units in May 2000.
Thereafter, any remaining Preference Units may, under certain circumstances, be
subject to redemption.
 
NOTE 5 -- RELATED PARTY TRANSACTIONS:
 
     Management fees. For the quarters ended March 31, 1999 and March 31, 1998,
the General Partner charged Leviathan $2.3 million and $2.5 million,
respectively, pursuant to Leviathan's partnership agreement which provides for
reimbursement of expenses the General Partner incurred, including reimbursement
of expenses incurred by El Paso Energy in providing management services to
Leviathan, its subsidiaries and the General Partner.
 
     Viosca Knoll System. Viosca Knoll system is currently owned 50% by a
subsidiary of Leviathan and 50% by El Paso Energy (through a wholly owned
subsidiary). Viosca Knoll is managed by a committee consisting of
representatives from each of the partners. Leviathan is the operator of Viosca
Knoll and has contracted with a wholly owned indirect subsidiary of El Paso
Energy to maintain the pipeline and with the General Partner to perform
financial, accounting and administrative services. The Viosca Knoll gathering
system interconnects with six interstate pipelines in the South Pass and Main
Pass areas of the Gulf. One of these interstate pipelines is owned by an
affiliate of El Paso Energy.
 
     In January 1999, Leviathan entered into an agreement to acquire all of El
Paso Energy's interest in Viosca Knoll, other than a 1% interest, for up to
$85.3 million (subject to adjustment), comprised of 25% in cash (up to a maximum
of $21.3 million) and 75% in Common Units (at least 2,647,826 Common Units), the
number of which will depend on the average closing price of Common Units during
the applicable trading reference period. At the closing, (i) El Paso Energy will
contribute approximately $33.4 million in cash to Viosca Knoll, which is 50% of
the principal amount outstanding under Viosca Knoll's credit facility, (ii)
Leviathan will deliver to El Paso Energy the cash and Common Units described
above and (iii) as required by Leviathan's partnership agreement, the General
Partner will contribute approximately $650,000 to Leviathan in order to maintain
its 1% capital account balance. Upon consummation of the acquisition,
Leviathan's partnership agreement will be amended to decrease the vote required
for approval of certain actions, including the removal of a general partner
without cause, from 66 2/3% to 55%.
 
     As a result of the acquisition, Leviathan will own 99% of Viosca Knoll and
will have the option to acquire the remaining 1% interest during the six-month
period commencing on the day after the first anniversary of that closing date.
The option price, payable in cash, is equal to the sum of $1.7 million plus the
amount of additional distributions which would have been paid, accrued or been
in arrears had Leviathan acquired the remaining 1% of Viosca Knoll at the
initial closing by issuing additional Common Units in lieu of a cash payment of
$1.7 million.
 
     The number of units actually issued by Leviathan in connection with the
acquisition of the additional interest in the Viosca Knoll transaction will be
determined by dividing $64 million (subject to adjustment) by the average
closing sales price for a Common Unit on the NYSE for the ten-day trading period
ending two days prior to the closing date (the "Market Price"); provided that,
for purposes of such calculation, the Market Price will not be less than $19.95
per Common Unit or more than $24.15 per Common Unit. Accordingly, Leviathan will
neither issue less than 2,647,826 nor more than 3,205,263 Common Units, subject
to adjustments contemplated by the definitive agreements. Based on the closing
sales price of the Common Units on May 10, 1999 of $22.25 per unit and certain
adjustments contemplated by the definitive agreements, Leviathan would issue
2,674,079 Common Units to El Paso Energy, which issuance would constitute
approximately 9.7% of the units (Common and Preference) outstanding immediately
after such issuance and would result in El Paso Energy owning, indirectly
through its subsidiaries, a combined 34.5% effective interest
 
                                        9
<PAGE>   11
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
in Leviathan, consisting of a 1% general partner interest, a 32.5% limited
partner interest comprised of 8,965,973 Common Units and an approximate 1%
nonmanaging interest in certain subsidiaries of Leviathan.
 
     In connection with the Viosca Knoll transaction, Leviathan has granted El
Paso Energy the right on three occasions during the three years after the
closing to require Leviathan to file a registration statement covering such
Common Units and to participate in offerings made pursuant to certain other
registration statements filed by Leviathan during a ten-year period. Such
registrations would be at Leviathan's expense and, generally, would allow El
Paso Energy to dispose of all or any of its Common Units without registration
under applicable security laws. If the acquisition is consummated, there can be
no assurance (i) regarding how long El Paso Energy may hold any of its Common
Units or (ii) whether or not El Paso Energy's disposition of a significant
number of Common Units in a short period of time would depress the market price
of the Common Units.
 
     Consummation of the acquisition is subject to the satisfaction of certain
closing conditions, including obtaining approval or consent from any required
third party. Management believes that the acquisition of the Viosca Knoll
interest does not require any federal, state or other regulatory approval. On
March 5, 1999, the Unitholders of record as of January 28, 1999, held a meeting
and ratified and approved the transactions based upon the ratification, approval
and recommendation of the board of directors of the General Partner and a
special committee of independent directors of the General Partner and based on a
fairness opinion of an independent advisor. Leviathan will need to obtain
consent of the lenders under the Leviathan Credit Facility and, if the Viosca
Knoll Credit Facility is not terminated immediately prior to consummating this
transaction, the lenders under that credit facility. There can be no assurance
that all such required consents will be obtained.
 
     If the remaining conditions to closing are satisfied, including obtaining
certain third party approvals and consents, management believes that the closing
of the acquisition of the Viosca Knoll interest will occur during the second
quarter of 1999.
 
  Other
 
     In January 1999, Leviathan issued 1,500 unit options at $20.625 per unit
option to an outside director under the 1998 Unit Option Plan for Non-Employee
Directors.
 
NOTE 6 -- COMMITMENTS AND CONTINGENCIES:
 
     Leviathan may utilize derivative financial instruments for purposes other
than trading to manage its exposure to movements in interest rates and commodity
prices. In accordance with procedures established by Leviathan's Board of
Directors, Leviathan monitors current economics conditions and evaluates its
expectations of future prices and interest rates when making decisions with
respect to risk management.
 
     Interest Rate Risk. Leviathan is exposed to some market risk due to the
floating interest rate under its credit facility. Under Leviathan's credit
facility, the remaining principal and the final interest payment are due in
December 1999. As of May 10, 1999, Leviathan's credit facility had a principal
balance of $350 million at an average floating interest rate of 7.2% per annum.
A 1.5% increase in interest rates could result in a $5.3 million annual increase
in interest expense on the existing principal balance. Leviathan is exposed to
similar risk under the credit facilities and loan agreements entered into by its
joint ventures. Leviathan has determined that it is not necessary to participate
in interest rate-related derivative financial instruments because it currently
does not expect significant short-term increases in the interest rates charged
under Leviathan's credit facility or the various joint venture credit facilities
and loan agreements.
 
     Commodity Price Risk. Leviathan hedges a portion of its oil and natural gas
production to reduce its exposure to fluctuations in the market prices thereof.
Leviathan uses commodity price swap transactions whereby monthly settlements are
based on differences between the prices specified in the commodity price swap
agreements and the settlement prices of certain futures contracts quoted on the
New York Mercantile
                                       10
<PAGE>   12
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
Exchange ("NYMEX") or certain other indices. Leviathan settles the commodity
price swap transactions by paying the negative difference or receiving the
positive difference between the applicable settlement price and the price
specified in the contract. The commodity price swap transactions Leviathan uses
differ from futures contracts in that there are no contractual obligations which
require or allow for the future delivery of the product. The credit risk from
Leviathan's price swap contracts is derived from the counter-party to the
transaction, typically a major financial institution. Leviathan does not require
collateral and does not anticipate non-performance by this counter-party, which
does not transact a sufficient volume of transactions with Leviathan to create a
significant concentration of credit risk. Gains or losses resulting from hedging
activities and the termination of any hedging instruments are initially deferred
and included as an increase or decrease to oil and natural gas sales in the
period in which the hedged production is sold. For the quarter ended March 31,
1999, Leviathan recorded a net loss of $0.4 million related to hedging
activities.
 
     As of March 31, 1999, Leviathan has open sales swap transactions for 10,000
million British thermal units ("MMbtu") of natural gas per day for calendar 2000
at a fixed price to be determined at its option equal to the February 2000
Natural Gas Futures Contract on the NYMEX as quoted at any time during 1999 and
January 2000, to and including the last two trading days of the February 2000
contract, minus $0.5450 per MMbtu. Additionally, Leviathan has open sales swap
transactions of 10,000 MMbtu of natural gas per day at a fixed price to be
determined at its option equal to the January 2000 Natural Gas Futures Contract
on NYMEX as quoted at any time during 1999, to and including the last two
trading days of the January 2000 contract, minus $0.50 per MMbtu.
 
     If Leviathan had settled its open natural gas hedging positions as of March
31, 1999 based on the applicable settlement prices of the NYMEX futures
contracts, Leviathan would have recognized a loss of approximately $2.6 million.
 
  Other
 
     Leviathan is involved from time to time in various claims, actions,
lawsuits and regulatory matters that have arisen in the ordinary course of
business, including various rate cases and other proceedings before the Federal
Energy Regulatory Commission.
 
     Leviathan and several subsidiaries of El Paso Energy have been made
defendants in actions brought by Jack Grynberg on behalf of the U.S. Government
under the false claims act. Generally, the complaints allege an industry-wide
conspiracy to underreport the heating value as well as the volumes of the
natural gas produced from federal and Indian lands, thereby depriving the U.S.
Government of royalties. In April 1999, the U.S. Government filed a notice that
it does not intend to intervene in these actions. Leviathan and El Paso Energy
believe the complaint is without merit and therefore will not have a material
adverse effect on Leviathan's consolidated financial position, results of
operations or cash flows.
 
     Leviathan is a defendant in a lawsuit filed by Transco Gas Pipe Line
Corporation ("Transco") in the 157th Judicial District Court, Harris County,
Texas on August 30, 1996. Transco alleges that, pursuant to a platform lease
agreement entered into on June 28, 1994, Transco has the right to expand its
facilities and operations on the offshore platform by connecting additional
pipeline receiving and appurtenant facilities. Management has denied Transco's
request to expand its facilities and operations because the lease agreement does
not provide for such expansion and because Transco's activities will interfere
with the Manta Ray Offshore system and Leviathan's existing and planned
activities on the platform. Transco has requested a declaratory judgment and is
seeking damages. The case is set for trial in June 1999. It is the opinion of
management that adequate defenses exist and that the final disposition of this
suit, will not have a material adverse effect on Leviathan's consolidated
financial position, results of operations or cash flows.
 
     Leviathan is a named defendant in numerous lawsuits and a named party in
numerous governmental proceedings arising in the ordinary course of business.
While the outcome of such lawsuits or other proceedings against Leviathan cannot
be predicted with certainty, management currently does not expect
                                       11
<PAGE>   13
             LEVIATHAN GAS PIPELINE PARTNERS, L.P. AND SUBSIDIARIES
 
      NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
these matters to have a material adverse effect on Leviathan's consolidated
financial position, results of operations, or cash flows.
 
NOTE 7 -- NEW ACCOUNTING PRONOUNCEMENT NOT YET ADOPTED:
 
     In June 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standard ("SFAS") No. 133, "Accounting for Derivative
Instruments and Hedging Activities." SFAS No. 133 requires that entities
recognize all derivative investments as either assets or liabilities on the
balance sheet and measure those instruments at fair value. Changes in the fair
value of derivatives are recorded each period in current earnings or other
comprehensive income, depending on whether a derivative is designated as a hedge
transaction. For fair-value hedge transactions in which Leviathan is hedging
changes in an asset's, liability's or firm commitment's fair value, changes in
the fair value of the derivative instrument will generally be offset in the
income statement by changes in the hedged item's fair value. For cash-flow hedge
transactions, in which Leviathan is hedging the variability of cash flows
related to a variable-rate asset, liability, or a forecasted transaction,
changes in the fair value of the derivative instrument will be reported in other
comprehensive income. The gains and losses on the derivative instrument that are
reported in other comprehensive income will be reclassified as earnings in the
periods in which earnings are impacted by the variability of the cash flows of
the hedged item. The ineffective portion of all hedges will be recognized in
current-period earnings. This statement is effective for fiscal years beginning
after June 15, 1999. Leviathan is currently evaluating the effects of this
pronouncement.
 
NOTE 8 -- NET INCOME (LOSS) PER UNIT:
 
     Basic and diluted net income (loss) per unit is calculated based upon the
net income (loss) of Leviathan less an allocation of net income to the General
Partner proportionate to its share of cash distributions and is presented below
for the quarter ended March 31 (in thousands).
 
<TABLE>
<CAPTION>
                                                    1999                           1998
                                         ---------------------------   ----------------------------
                                         LIMITED    GENERAL            LIMITED    GENERAL
                                         PARTNERS   PARTNER   TOTAL    PARTNERS   PARTNER    TOTAL
                                         --------   -------   ------   --------   -------   -------
<S>                                      <C>        <C>       <C>      <C>        <C>       <C>
Net income (loss)(a)...................  $ 3,464     $ 35     $3,499   $(1,410)    $ (14)   $(1,424)
Allocation to General Partner(b).......     (628)     628         --       261      (261)        --
                                         -------     ----     ------   -------     -----    -------
Allocation of net income (loss) as
  adjusted for incentive
  distributions........................  $ 2,836     $663     $3,499   $(1,149)    $(275)   $(1,424)
                                         =======     ====     ======   =======     =====    =======
Weighted average number of units
  outstanding(c).......................   24,367                        24,367
                                         =======                       =======
Basic and diluted net income (loss) per
  unit.................................  $  0.12                       $ (0.05)
                                         =======                       =======
</TABLE>
 
---------------
 
(a)  Net income (loss) allocated 99% to the limited partners as holders of the
     Preference and Common Units and 1% to the General Partner.
 
(b)  Represents allocation of net income (loss) to the General Partner
     proportionate to its share of each quarter's cash distributions which
     included incentive distributions (Note 4).
 
(c)  Diluted weighted average number of units outstanding is less than 1
     thousand units higher than basic weighted average units outstanding as a
     result of unit options included in the diluted weighted average. Diluted
     average number of units outstanding excludes 933 thousand outstanding unit
     options to purchase an equal number of Common Units of Leviathan, as the
     exercise prices of these unit options were greater than the average market
     price of the Common Units.
 
                                       12
<PAGE>   14
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS
 
     The information contained in Item 2 updates, and should be read in
conjunction with, information set forth in Part II, Items 7, 7A and 8 in the
Leviathan Annual Report on Form 10-K for the year ended December 31, 1998, in
addition to the interim condensed consolidated financial statements and
accompanying notes presented in Item 1 of this Form 10-Q. Unless the context
otherwise requires, all references herein to Leviathan with respect to the
operations and ownership of Leviathan's assets are also references to its
subsidiaries.
 
OVERVIEW
 
     Leviathan, a publicly held Delaware master limited partnership, is a
provider of integrated energy services, including natural gas and oil gathering,
transportation, midstream and other related services in the Gulf. Through its
subsidiaries and joint ventures, Leviathan owns interests in significant assets,
including (i) the Gas Pipelines, (ii) a crude oil pipeline system, (iii) six
strategically-located multi-purpose platforms, (iv) production handling and
dehydration facilities, (v) four producing oil and natural gas properties and
(vi) a non-producing oil and natural gas property, the Ewing Bank 958 Unit,
comprised of Ewing Bank Blocks 958, 959, 1002 and 1003.
 
     The Gas Pipelines, located primarily offshore Louisiana, Mississippi and
eastern Texas, gather and transport natural gas for producers, marketers,
pipelines and end-users for a fee. Leviathan's interest in the Gas Pipelines
consists of: a 100% interest in each of Green Canyon Pipe Line Company, L.L.C.
and Tarpon Transmission Company; a 50% interest in each of Stingray and Viosca
Knoll; an indirect 40% interest in each of HIOS and East Breaks; a 33.3%
interest in UTOS; and an effective 25.67% interest in each of Manta Ray Offshore
and Nautilus. The Gas Pipelines include approximately 1,200 miles of pipeline
with a throughput capacity of approximately 6.8 billion cubic feet of natural
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.
 
     Leviathan owns a 36% interest in POPCO, which owns and operates the
Poseidon oil pipeline. The Poseidon oil pipeline is located primarily offshore
Louisiana and consists of approximately 300 miles of pipeline with a throughput
capacity of 400 million barrels of oil per day.
 
     Leviathan operates and owns interests in six strategically-located
multi-purpose platforms in the Gulf, including a 100% interest in five
platforms -- Viosca Knoll Block 817, East Cameron Block 373, Ship Shoal Block
332, South Timbalier Block 292 and Ship Shoal Block 331 -- and a 50% interest in
the Garden Banks Block 72 Platform. These platforms have production handling
capabilities which complement Leviathan's pipeline operations and play a key
role in the development of oil and natural 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.
In addition, Leviathan owns a 50% interest in West Cameron Dehy, a dehydration
and production handling facility located at the terminus of the Stingray system,
onshore Louisiana.
 
     Leviathan owns an interest in four producing oil and natural gas leases in
the Gulf. The Viosca Knoll Block 817 wells (100% working interest, subject to a
production payment obligation) are currently producing a gross aggregate average
of approximately 42 million cubic feet ("MMcf") of natural gas per day. As of
May 10, 1999, (i) the Garden Banks Block 72 wells (50% working interest) are
producing a gross aggregate average of approximately 1,440 barrels of oil and 4
MMcf of natural gas per day, (ii) the Garden Banks Block 117 wells (50% working
interest) are producing a gross aggregate average of approximately 1,140 barrels
of oil and 2 MMcf of natural gas per day and (iii) the West Delta Block 35 wells
(38% working interest) are producing 11 barrels of oil and 8 MMcf of natural gas
per day.
 
                                       13
<PAGE>   15
 
RESULTS OF OPERATIONS
 
  Quarter Ended March 31, 1999 Compared With Quarter Ended March 31, 1998
 
     Net income for the quarter ended March 31, 1999 totaled $3.5 million, or
$0.12 per unit, as compared with a net loss of $1.4 million, or $0.05 per unit,
for the quarter ended March 31, 1998 as a result of the items discussed below.
 
     Oil and natural gas sales totaled $6.8 million for the quarter ended March
31, 1999, as compared with $9.1 million for the same period in 1998. The
decrease is attributable to (i) substantially lower realized oil and natural gas
prices and (ii) normal production declines from Leviathan's oil and natural gas
properties, partially offset by production from properties acquired in August
1998. During the quarter ended March 31, 1999, Leviathan produced and sold 3,585
MMcf of natural gas and 99,237 barrels of oil at average prices of $1.60 per
thousand cubic feet ("Mcf") and $10.46 per barrel, respectively. During the same
period in 1998, Leviathan produced and sold 2,789 MMcf of natural gas and
170,095 barrels of oil at average prices of $2.20 per Mcf and $17.26 per barrel,
respectively.
 
     Revenue from gathering, transportation and platform services totaled $4.4
million for the quarter ended March 31, 1999 as compared with $3.3 million for
the same period in 1998. The increase primarily reflects an increase of $2.1
million in platform services revenue from Leviathan's East Cameron Block 373
platform which was placed in service in April 1998, offset by decreases of (i)
$0.6 million in gathering revenues as a result of lower throughput on the Green
Canyon and Tarpon systems and (ii) $0.4 million in platform services revenue
from Leviathan's Viosca Knoll Block 817 platform as a result of lower third
party platform access fees as a result of Leviathan's acquisition of additional
working interests in the Viosca Knoll Block 817 property in August 1998.
 
     Revenue from equity in earnings totaled $10.7 million for the quarter ended
March 31, 1999, as compared with $5.3 million for the same period in 1998. The
increase of $5.4 million primarily reflects increases of (i) $0.9 million
related to Stingray as a result of changes in prior period estimates of reserves
for uncollectable revenues and (ii) $4.5 million from POPCO, Viosca Knoll,
Nautilus and Manta Ray Offshore as a result of increased throughput. Total
natural gas throughput volumes for the Equity Investees increased approximately
6.9% from the quarter ended March 31, 1998 to the same period in 1999 primarily
as a result of increased throughput on the Viosca Knoll, Nautilus and Manta Ray
Offshore systems. Oil volumes from Poseidon totaled 13.4 million barrels and 6.7
million barrels for the quarter ended March 31, 1999 and 1998, respectively.
 
     Depreciation, depletion and amortization totaled $6.7 million for the
quarter ended March 31, 1999, as compared with $7.9 million for the same period
in 1998. The decrease of $1.2 million reflects a decrease of $1.5 million in
depreciation and depletion of oil and natural 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 depletion and abandonment accrual rates offset by
$0.3 million of depreciation on Leviathan's East Cameron Block 373 and Ship
Shoal Block 331 platforms placed in service after March 31, 1998.
 
     General and administrative expenses, including the General Partner's
management fee, totaled $3.1 million for the quarter ended March 31, 1999, as
compared with $5.0 million for the same period in 1998. The decrease of $1.9
million reflects decreases of (i) $0.2 million in the General Partner's
management fees and (ii) $1.7 million in direct general and administrative
expenses of Leviathan in the 1998 period primarily related to the appreciation
and vesting of unit rights granted to certain officers and employees under a
compensation plan that was terminated in October 1998.
 
     Interest and other financing costs, excluding capitalized interest, for the
quarter ended March 31, 1999, totaled $6.1 million as compared with $3.7 million
for the same period in 1998. During the quarter ended March 31, 1999 and 1998,
Leviathan capitalized $0.4 million and $0.5 million, respectively, of interest
costs in connection with construction projects and drilling activities in
progress during such periods. During the quarter ended March 31, 1999 and 1998,
Leviathan had outstanding indebtedness averaging approximately $347.3 million
and $244.5 million, respectively.
 
                                       14
<PAGE>   16
 
LIQUIDITY AND CAPITAL RESOURCES
 
     Sources of Cash. Leviathan intends to satisfy its capital requirements and
other working capital needs primarily from cash on hand, cash from operations
and borrowings under the Leviathan Credit Facility (discussed below). However,
depending on market and other factors, Leviathan may issue additional equity to
raise cash or acquire assets, such as the proposed acquisition of the additional
interest in Viosca Knoll. Net cash provided by operating activities for the
quarter ended March 31, 1999, totaled $10.0 million. In addition to funds
available under the Leviathan Credit Facility or from the issuance of equity,
Leviathan may use debt securities to raise cash to fund its working capital
requirements, including funding the cash portion of the purchase price of the
additional interest in Viosca Knoll and to repay the borrowings under the Viosca
Knoll Credit Facility. At March 31, 1999, Leviathan had cash and cash
equivalents of $6.4 million.
 
     Cash from operations is derived from (i) payments for gathering and
transportation of natural gas through Leviathan's 100% owned pipelines, (ii)
platform access and production handling fees, (iii) cash distributions from
Equity Investees and (iv) the sale of oil and natural gas attributable to
Leviathan's interest in its producing properties. Oil and natural gas properties
are depleting assets and will produce reduced volumes of oil and natural gas in
the future unless additional wells are drilled or recompletions of existing
wells are successful. See "Overview" for current production rates from
Leviathan's properties.
 
     Leviathan'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, Western Gulf, 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 Leviathan from Equity
Investees during the quarter ended March 31, 1999, totaled $10.1 million.
 
     The Leviathan Credit Facility is a revolving credit facility with a
syndicate of commercial banks providing for up to $375 million of available
credit, subject to customary terms and conditions, including certain limitations
on incurring additional indebtedness (including borrowings under this facility)
if certain financial targets are not achieved and maintained. In addition,
Leviathan will be required to prepay a portion of the balance outstanding under
this credit facility to the extent such financial targets are not achieved and
maintained. Proceeds from the Leviathan Credit Facility are available to
Leviathan for general partnership purposes, including financing capital
expenditures, working capital requirements and, subject to certain limitations,
distributions to the unitholders. The Leviathan 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 Leviathan Credit
Facility matures in December 1999; is guaranteed by the General Partner and each
of Leviathan's subsidiaries; and is collateralized by (i) the management
agreement between the General Partner and a subsidiary of El Paso Energy, (ii)
substantially all of the assets of Leviathan and (iii) the General Partner's 1%
general partner interest in Leviathan and approximate 1% nonmanaging interest in
certain subsidiaries of Leviathan. The Leviathan Credit Facility has no
scheduled amortization prior to maturity. As of March 31, 1999, Leviathan had
$355 million outstanding under its credit facility bearing interest at an
average floating rate of 7.2% per annum. As of May 10, 1999, Leviathan had $350
million outstanding and approximately $25 million of funds available under this
credit facility. Leviathan has executed a commitment letter with a group of the
current lenders under the Leviathan Credit Facility to amend and extend this
facility, which management expects to complete on or before the maturity date of
the current facility.
 
     Viosca Knoll has a revolving credit facility, as amended, (the "Viosca
Knoll Credit Facility") with a syndicate of commercial banks to provide up to
$100 million for working capital needs of Viosca Knoll. Viosca Knoll's ability
to borrow money under its credit facility is subject to certain customary terms
and conditions, including certain limitations on incurring additional
indebtedness (including borrowings under this credit facility) if certain
financial targets are not achieved and maintained. In addition, Viosca Knoll
will be required to prepay a portion of the balance outstanding under this
credit facility to the extent such financial targets are not achieved and
maintained. The Viosca Knoll Credit Facility is collateralized by all of Viosca
Knoll's material contracts and agreements, receivables and inventory and matures
on December 20, 2001. In addition, under certain circumstances, each partner in
Viosca Knoll has agreed to return up to $2.5 million in
 
                                       15
<PAGE>   17
 
distributions paid to it by Viosca Knoll. The Viosca Knoll Credit Facility has
no scheduled amortization prior to maturity. As of March 31, 1999, Viosca Knoll
had $66.7 million outstanding under its credit facility bearing interest at an
average floating rate of 6.0% per annum. As of May 10, 1999 Viosca Knoll had
$66.7 million outstanding and approximately $33.3 million of funds available
under its credit facility. Concurrent with the closing of the acquisition of the
additional interest in Viosca Knoll discussed in Item 1. Financial Statements,
Note 5 -- Related Party Transactions -- Viosca Knoll System, El Paso Energy will
contribute approximately $33.4 million to Viosca Knoll to use to pay down 50% of
the principal balance outstanding under the Viosca Knoll Credit Facility, and
Leviathan expects to pay the remaining outstanding balance using available funds
and cancel the Viosca Knoll Credit Facility.
 
     POPCO has a revolving credit facility, as amended, (the "POPCO Credit
Facility") with a syndicate of commercial banks to provide up to $150 million
for working capital needs of POPCO. POPCO's ability to borrow money under the
facility is subject to certain customary terms and conditions, including certain
limitations on incurring additional indebtedness (including borrowings under
this credit facility) if certain financial targets are not achieved and
maintained. In addition, POPCO will be required to prepay a portion of the
balance outstanding under this credit facility to the extent such financial
targets are not achieved and maintained. The POPCO Credit Facility has no
scheduled amortization prior to maturity. The POPCO Credit Facility is
collateralized by a substantial portion of POPCO's assets and matures on April
30, 2001. As of March 31, 1999, POPCO had $136.5 million outstanding under its
credit facility bearing interest at an average floating rate of 6.25% per annum.
As of May 10, 1999, POPCO had approximately $136.5 million outstanding and
approximately $13.5 million of funds available under this credit facility.
 
     Stingray has an existing term loan agreement with a syndicate of commercial
banks which matures on March 31, 2003. The agreement requires Stingray to make
18 quarterly principal payments of approximately $1.6 million commencing
December 31, 1998. The term loan agreement is principally collateralized by
current and future natural gas transportation contracts between Stingray and its
customers. On the earlier to occur of March 31, 2003 or the accelerated due date
pursuant to the Stingray credit agreement, if Stingray has not paid all amounts
due under its credit agreement, Leviathan is obligated to pay the lesser of (i)
$8.5 million, (ii) the aggregate amount of distributions received by Leviathan
from Stingray subsequent to January 1, 1998 or (iii) 50% of any then outstanding
amounts due pursuant to the Stingray credit agreement. Leviathan does not expect
to have to pay any amount pursuant to this obligation. As of March 31, 1999,
Stingray had $25.3 million outstanding under its term loan agreement bearing
interest at an average floating rate of 6.25% per annum.
 
     Western Gulf, which owns all of HIOS and East Breaks, entered into a
revolving credit facility (the "Western Gulf Credit Facility") with a syndicate
of commercial banks in February 1999 to provide up to $100 million for the
construction of the East Breaks system and for other working capital needs of
Western Gulf, East Breaks and HIOS. Western Gulf's ability to borrow money under
its credit facility is subject to certain customary terms and conditions,
including certain limitations on incurring additional indebtedness (including
borrowings under this credit facility) if certain financial targets are not
achieved and maintained. In addition, Western Gulf would be required to prepay a
portion of the balance outstanding under this credit facility to the extent such
financial targets are not achieved and maintained. The Western Gulf Credit
Facility has no scheduled amortization prior to its maturity in February 2004.
The Western Gulf Credit Facility is collateralized by substantially all of the
material contracts and agreements of East Breaks and Western Gulf, including
Western Gulf's ownership in HIOS and East Breaks, and supported by a guarantee
of East Breaks. In addition, Leviathan has agreed to return up to $2.0 million
in distributions paid to Leviathan by Western Gulf under certain circumstances.
As of March 31, 1999, Western Gulf had $44.1 million outstanding under this
credit facility bearing interest at a floating rate of 6.4% per annum. As of May
10, 1999 Western Gulf had $47.1 million outstanding and approximately $52.9
million of funds available under this facility.
 
     Uses of Cash. Leviathan's capital requirements consist primarily of (i)
quarterly distributions to holders of Preference Units and Common Units and to
the 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 energy-related infrastructure in
the Gulf, (iii) expenditures related to its producing oil and natural gas
properties, (iv) expenditures relating to the development of its non-producing
                                       16
<PAGE>   18
 
property, the Ewing Bank 958 Unit, (v) administrative expenses (including
management fees) and other operating expenses, (vi) contributions to Equity
Investees as required to fund capital expenditures for new facilities and (vii)
debt service on its outstanding indebtedness.
 
     On April 20, 1999, Leviathan declared its first quarter cash distribution
of $0.275 per Preference Unit and $0.525 per Common Unit. The distributions were
paid on May 14, 1999, to all holders of record of Common Units and Preference
Units at the close of business on April 30, 1999. These quarterly distributions
cover the period from January 1, 1999 through March 31, 1999. Leviathan believes
that it will be able to continue to pay at least the current quarterly cash
distributions of $0.275 per Preference Unit and $0.525 per Common Unit for the
foreseeable future. At these distribution rates, the quarterly distributions
total $15.6 million ($17.4 million assuming the issuance of at least 2,647,826
common units upon the consummation of the Viosca Knoll transaction) in respect
to the Preference Units, Common Units and the general partner interests. During
the quarter ended March 31, 1999, Leviathan paid the General Partner incentive
distributions totaling $2.8 million and in May 1999 paid the General Partner an
incentive distribution of $2.8 million for the quarter ended March 31, 1999.
 
     East Breaks is currently constructing a natural gas pipeline system which
will initially consist of 85 miles of an 18 to 20-inch pipeline and related
facilities connecting the Diana and Hoover prospects developed by Exxon
Corporation ("Exxon") and BP Amoco Plc ("BP Amoco") in Alaminos Canyon Block 25
in the Gulf with the HIOS system. The majority of the construction of the East
Breaks system will occur in 1999 and the system is anticipated to be in service
in mid 2000 at an estimated cost of approximately $90 million. East Breaks
entered into long-term agreements with Exxon and BP Amoco involving the
commitment, gathering and processing of production from the Diana and Hoover
prospects. Substantially all of the construction costs of the East Breaks system
will be funded by the Western Gulf Credit Facility. All of the natural gas to be
produced from 11 blocks in the East Breaks and Alaminos Canyon areas will be
dedicated for transportation services on the HIOS system.
 
     Substantially all of the capital expenditures by POPCO, Viosca Knoll, East
Breaks, and Stingray were funded by borrowings under credit facilities, and any
future capital expenditures by East Breaks, POPCO, Viosca Knoll, HIOS and
Stingray are anticipated to be funded by borrowings under credit facilities. As
discussed above, concurrent with the closing of the acquisition of the
additional interest in Viosca Knoll, Leviathan expects to repay in full and
terminate the Viosca Knoll Credit Facility. Leviathan's capital expenditures
(including construction and installation costs of a 40-mile, 14-inch crude oil
pipeline from Ship Shoal Block 332 to Green Canyon Block 253 (the "Allegheny oil
pipeline") and development costs of the Ewing Bank 958 Unit) and equity
investments for the quarter ended March 31, 1999 were $6.5 million. Leviathan
has in the past contributed existing assets to joint ventures as partial
consideration for its ownership interest therein and may in the future
contribute existing assets, including cash, to new joint ventures as partial
consideration for its ownership interest therein.
 
     Interest costs incurred by Leviathan related to the Leviathan Credit
Facility totaled $6.5 million for the quarter ended March 31, 1999. Leviathan
capitalized $0.4 million of such interest costs in connection with construction
projects and drilling activities in progress during the period.
 
     Leviathan anticipates that its capital expenditures and equity investments
for the remainder of 1999 will relate to continuing acquisition, construction
and development activities, including consummating the acquisition of the
additional interest in Viosca Knoll, the completion of the Allegheny oil
pipeline, and the development of the Ewing Bank 958 Unit. Leviathan anticipates
funding such cash requirements primarily with available cash flow, borrowings
under the Leviathan Credit Facility and, depending on the capital requirements
and related market conditions, issuing additional debt and/or equity.
 
YEAR 2000
 
     The Year 2000 issue is the result of computer programs that were written
using two digits rather than four to define the year. Leviathan has established
a project team and works with the El Paso Energy executive steering committee to
coordinate the phases of its Year 2000 project to ensure that Leviathan's key
automated systems and related processes will remain functional through Year
2000. Those phases include: (i) awareness,
                                       17
<PAGE>   19
 
(ii) assessment, (iii) remediation, (iv) testing, (v) implementation of the
necessary modifications and (vi) contingency planning (which was previously
included as a component of Leviathan's implementation phase). Leviathan has
hired outside consultants and is involved in several industry trade-groups to
supplement Leviathan's project team.
 
     The awareness phase recognizes the importance of Year 2000 issues and its
potential impact on Leviathan. Through the project team, Leviathan has
established an awareness program which includes participation of management in
each business area. The awareness phase is substantially completed, although
Leviathan will continually update awareness efforts for the duration of the Year
2000 project.
 
     The assessment phase consists of conducting an inventory of Leviathan's key
automated systems and related processes, analyzing and assigning levels of
criticality to those systems and processes, identifying and prioritizing
resource requirements, developing validation strategies and testing plans, and
evaluating business partner relationships. Leviathan estimates that it is more
than three-quarters of the way complete with the portion of the assessment phase
to determine the nature and impact of the Year 2000 date change for hardware and
equipment, embedded chip systems, and third-party developed software. The
assessment phase of the project involves, among other things, efforts to obtain
representations and assurances from third parties, including Equity Investees,
partners and third party customers and vendors, that their hardware and
equipment products, embedded chip systems and software products being used by or
impacting Leviathan are or will be modified to be Year 2000 compliant. To date,
the responses from such third parties, although generally encouraging, are
inconclusive. Although Leviathan intends to interact only with those third
parties that have Year 2000 compliant computer systems, it is impossible for
Leviathan to monitor all such systems. As a result, Leviathan cannot predict the
potential consequences if its Equity Investees, partners, customers or vendors
are not Year 2000 compliant. Leviathan is currently evaluating the exposure
associated with such business partner relationships.
 
     The remediation phase involves converting, modifying, replacing or
eliminating selected key automated systems identified in the assessment phase.
The testing phase involves the validation of the identified key automated
systems. Leviathan is utilizing test tools and written procedures to document
and validate, as necessary, its unit, system, integration and acceptance
testing. Leviathan estimates that approximately three-quarters of the work for
these phases is complete, and expects each phase to be substantially completed
by mid-1999.
 
     The implementation phase involves placing the converted or replaced key
automated systems into operation. In some cases, the implementation phase will
also involve the implementation of contingency plans needed to support business
functions and processes that may be interrupted by Year 2000 failures that are
outside Leviathan's control. Leviathan is more than half way complete with this
phase and expects to be substantially completed by mid-1999.
 
     The contingency planning phase consists of developing a risk profile of
Leviathan's critical business processes and then providing for actions Leviathan
will pursue to keep such processes operational in the event of Year 2000
disruptions. The focus of such contingency planning is on prompt response to any
Year 2000 events, and a plan for subsequent resumption of normal operations. The
plan is expected to assess the risk of significant failure to critical processes
performed by Leviathan, and to address the mitigation of those risks. The plan
will also consider any significant failures in the event the most reasonably
likely worst case scenario develops, as discussed below. In addition, the plan
is expected to factor in the severity and duration of the impact of a
significant failure. Leviathan anticipates to complete its contingency plan by
mid-1999. This Year 2000 contingency plan will continue to be modified and
adjusted through the year as additional information from key external business
partners becomes available.
 
     Leviathan's goal is to ensure that all of its critical systems and
processes that are under its direct control remain functional. Certain systems
and processes may be interrelated with or dependent upon systems outside
Leviathan's control and systems within Leviathan's control may have unpredicted
problems. Accordingly, there can be no assurance that significant disruptions
will be avoided. Leviathan's present analysis of its most reasonably likely
worst case scenario for Year 2000 disruptions includes Year 2000 failures in the
telecommunications and electricity industries, as well as interruptions from
suppliers that might cause
                                       18
<PAGE>   20
 
disruptions in Leviathan's operations, thus causing temporary financial losses
and an inability to meet its obligations to customers. A significant portion of
the oil and natural gas transported through the pipelines is owned by third
parties. Accordingly, failures of the producers of oil and natural gas to be
ready for the Year 2000 could significantly disrupt the flow of the hydrocarbons
for customers. In many cases, the producers have no direct contractual
relationship with Leviathan, and Leviathan relies on its customers to verify the
Year 2000 readiness of the producers from whom they purchase oil and natural
gas. A portion of Leviathan's revenue for the transportation of oil and natural
gas is based upon fees paid by its customers for the reservation of capacity and
a portion of the revenue is based upon the volume of actual throughput. As such,
short-term disruptions in throughput caused by factors beyond Leviathan's
control may have a financial impact on Leviathan and could cause operational
problems for Leviathan's customers. Longer-term disruptions could materially
impact Leviathan's operations, financial condition and cash flows.
 
     While the total cost of Leviathan's Year 2000 project is still being
evaluated, Leviathan estimates that the costs to be incurred in 1999 and 2000
associated with assessing, remediating and testing hardware and equipment,
embedded chip systems, and third-party developed software will not exceed $1.0
million, all of which will be expensed. As of March 31, 1999, Leviathan had
incurred less than $0.1 million related to such costs. Leviathan has previously
only tracked incremental expenses related to its Year 2000 project. The costs of
the Year 2000 project related to salaried employees of El Paso Energy, including
their direct salaries and benefits, are not available and have not been included
in the estimated costs of the project. The management fee charged to Leviathan
by the General Partner includes such incremental expenses. Since the earlier
phases of the Year 2000 project mostly involved the work performed by such
salaried employees, the costs expended to date do not reflect the percentage
completion of the project. Leviathan anticipates that it will expend most of the
costs reported above in the remediation, implementation and contingency planning
phases of the project.
 
     Presently, Leviathan intends to reassess its estimate of Year 2000 costs in
the event Leviathan completes an acquisition of, or makes a material investment
in, substantial facilities or another business entity.
 
     Management does not expect the costs of Leviathan's Year 2000 project will
have a material adverse effect on Leviathan's financial position, results of
operations or cash flows. However, based on information available at this time,
Leviathan cannot conclude that disruption caused by internal or external Year
2000 related failures will not adversely effect Leviathan. Specific factors
which may affect the success of Leviathan's Year 2000 efforts and the frequency
or severity of a Year 2000 disruption or amount of any expense include failure
of Leviathan or its outside consultants to properly identify deficient systems,
the failure of the selected remedial action to adequately address the
deficiencies, the failure of Leviathan's outside consultants to complete the
remediation in a timely manner (due to shortages of qualified labor or other
factors), the failure of other parties to joint ventures in which Leviathan is
involved to meet their obligations, both financial and operational under the
relevant joint venture agreements to remediate assets used by the joint venture,
unforeseen expenses related to the remediation of existing systems or the
transition to replacement systems, and the failure of third parties, including
Equity Investees, to become Year 2000 compliant or to adequately notify
Leviathan of potential noncompliance.
 
     The above disclosure is a "Year 2000 Readiness Disclosure" made with the
intention to comply fully with the Year 2000 Information and Readiness
Disclosure Act of 1998, Pub. L. No. 105-271, 112 Stat, 2386, signed into law
October 19, 1998. All statements made herein shall be construed within the
confines of the Act. To the extent that any reader of the above Year 2000
Readiness Disclosure is other than an investor or potential investor in
Leviathan's or an affiliate's equity or debt securities, this disclosure is made
for the sole purpose of communicating or disclosing information aimed at
correcting, helping to correct and/or avoiding Year 2000 failures.
 
UNCERTAINTY OF FORWARD-LOOKING STATEMENTS AND INFORMATION
 
     This Quarterly Report contains forward-looking statements and information
within the meaning of the Private Securities Litigation Reform Act of 1995 and
are based on management's beliefs as well as assumptions made by and information
currently available to management. Such statements are typically
 
                                       19
<PAGE>   21
 
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 Leviathan's
financial position, results of operations, and cash flows are:
 
     - competitive practices in the industry in which Leviathan competes,
 
     - the impact of current and future laws and government regulations
       affecting the industry in general and Leviathan's operations in
       particular,
 
     - environmental liabilities to which Leviathan may become subject in the
       future that are not covered by an indemnity or insurance,
 
     - the throughput levels achieved by any pipelines in which Leviathan owns
       (now or in the future) an interest,
 
     - the ability to access additional reserves to offset the natural decline
       in production from existing wells connected to such pipelines,
 
     - changes in gathering, transportation, processing, handling and other
       rates due to changes in government regulation and/or competitive factors,
 
     - the impact of oil and natural gas price fluctuations,
 
     - the production rates and reserve estimates associated with Leviathan's
       producing oil and natural gas properties,
 
     - significant changes from expectations of capital expenditures and
       operating expenses and unanticipated project delays,
 
     - the ability of Equity Investees to make distributions to Leviathan,
 
     - the effect of the Year 2000 date change,
 
     - Leviathan's consummation of the proposed acquisition of an additional
       interest in Viosca Knoll,
 
     - the ability to economically raise capital (debt and equity) to satisfy
       planned and unanticipated needs, and
 
     - other factors discussed more completely in Leviathan's other filings with
       the Securities and Exchange Commission.
 
     Leviathan disclaims any obligation to update any forward-looking statements
to reflect events or circumstances after the date hereof.
 
ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK
 
     Leviathan may utilize derivative financial instruments for purposes other
than trading to manage its exposure to movements in interest rates and commodity
prices. In accordance with procedures established by Leviathan's Board of
Directors, Leviathan monitors current economics conditions and evaluates its
expectations of future prices and interest rates when making decisions with
respect to risk management.
 
     Interest Rate Risk. Leviathan is exposed to some market risk due to the
floating interest rate under its credit facility. Under the Leviathan Credit
Facility, the remaining principal and the final interest payment are due in
December 1999. As of May 10, 1999, Leviathan's credit facility had a principal
balance of $350 million at an average floating interest rate of 7.2% per annum.
A 1.5% increase in interest rates could result in a $5.3 million annual increase
in interest expense on the existing principal balance. Leviathan is exposed to
similar risk under the credit facilities and loan agreements entered into by its
joint ventures. Leviathan has
                                       20
<PAGE>   22
 
determined that it is not necessary to participate in interest rate-related
derivative financial instruments because it currently does not expect
significant short-term increases in the interest rates charged under Leviathan's
credit facility or the various joint venture credit facilities and loan
agreements.
 
     Commodity Price Risk. Leviathan hedges a portion of its oil and natural gas
production to reduce its exposure to fluctuations in the market prices thereof.
Leviathan uses commodity price swap transactions whereby monthly settlements are
based on differences between the prices specified in the commodity price swap
agreements and the settlement prices of certain futures contracts quoted on the
NYMEX or certain other indices. Leviathan settles the commodity price swap
transactions by paying the negative difference or receiving the positive
difference between the applicable settlement price and the price specified in
the contract. The commodity price swap transactions Leviathan uses differ from
futures contracts in that there are no contractual obligations which require or
allow for the future delivery of the product. The credit risk from Leviathan's
price swap contracts is derived from the counter-party to the transaction,
typically a major financial institution. Leviathan does not require collateral
and does not anticipate non-performance by this counter-party, which does not
transact a sufficient volume of transactions with Leviathan to create a
significant concentration of credit risk. Gains or losses resulting from hedging
activities and the termination of any hedging instruments are initially deferred
and included as an increase or decrease to oil and natural gas sales in the
period in which the hedged production is sold. For the quarter ended March 31,
1999, Leviathan recorded a net loss of $0.4 million related to hedging
activities.
 
     As of March 31, 1999, Leviathan has open sales swap transactions for 10,000
MMbtu of natural gas per day for calendar 2000 at a fixed price to be determined
at its option equal to the February 2000 Natural Gas Futures Contract on NYMEX
as quoted at any time during 1999 and January 2000, to and including the last
two trading days of the February 2000 contract, minus $0.5450 per MMbtu.
Additionally, Leviathan has open sales swap transactions of 10,000 MMbtu of
natural gas per day at a fixed price to be determined at its option equal to the
January 2000 Natural Gas Futures Contract on NYMEX as quoted at any time during
1999, to and including the last two trading days of the January 2000 contract,
minus $0.50 per MMbtu.
 
     If Leviathan had settled its open natural gas hedging positions as of March
31, 1999 based on the applicable settlement prices of the NYMEX futures
contracts, Leviathan would have recognized a loss of approximately $2.6 million.
 
                           PART II. OTHER INFORMATION
 
ITEM 1. LEGAL PROCEEDINGS
 
     Note 6, Other.
 
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
 
     On March 5, 1999, Leviathan's unitholders of record as of January 28, 1999,
held a special meeting and ratified and approved the transaction involved in
Leviathan's acquisition of an additional interest in Viosca Knoll from El Paso
Energy. 13,098,873 votes were cast for the transaction, 93,118 against and
151,544 votes abstained. In addition, Leviathan's unitholders approved an
amendment to reduce the total votes of unitholders required to remove a general
partner from 66 2/3% to 55%. Such amendment will be implemented concurrently
with the closing of the acquisition of the interest in Viosca Knoll.
 
                                       21
<PAGE>   23
 
ITEM 5. OTHER INFORMATION
 
     None.
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
     (a) Exhibits
 
     Each exhibit identified below is filed as part of this quarterly report.
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
           27.           -- Financial Data Schedule.
</TABLE>
 
     (b) Reports on Form 8-K
 
     None.
 
                                       22
<PAGE>   24
 
                                   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.
 
                                          By: LEVIATHAN GAS PIPELINE COMPANY,
                                            its General Partner
 
                                          By:      /s/ KEITH B. FORMAN
                                            ------------------------------------
                                                      Keith B. Forman
                                                  Chief Financial Officer
 
Date: May 14, 1999
 
                                          By:      /s/ D. MARK LELAND
                                            ------------------------------------
                                                       D. Mark Leland
                                               Vice President and Controller
                                               (Principal Accounting Officer)
 
Date: May 14, 1999
 
                                       23
<PAGE>   25
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
           27.           -- Financial Data Schedule.
</TABLE>