<PAGE>   1
                                                                   EXHIBIT 10.1
 



                             LEVIATHAN GAS PIPELINE
                                 PARTNERS, L.P.
 
                           1998 OMNIBUS COMPENSATION
                                      PLAN
 
                        EFFECTIVE AS OF AUGUST 14, 1998
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                               TABLE OF CONTENTS
 
<TABLE>
<S>      <C>     <C>                                                           <C>
SECTION   1      PURPOSES....................................................    1
SECTION   2      DEFINITIONS.................................................    1
          2.1    Beneficiary.................................................    1
          2.2    Board of Directors..........................................    1
          2.3    Cause.......................................................    1
          2.4    Code........................................................    2
          2.5    Common Units................................................    2
          2.6    Company.....................................................    2
          2.7    Exchange Act................................................    2
          2.8    Fair Market Value...........................................    2
          2.9    General Partner.............................................    2
          2.10   Management Committee........................................    2
          2.11   Maximum Annual Employee Grant...............................    2
          2.12   Participant.................................................    2
          2.13   Performance Goals...........................................    2
          2.14   Performance Period..........................................    2
          2.15   Permanent Disability or Permanently Disabled................    3
          2.16   Plan Administrator..........................................    3
          2.17   Restricted Units............................................    3
          2.18   Rule 16b-3..................................................    3
          2.19   Section 16 Insider..........................................    3
          2.20   Subsidiary..................................................    3
          2.21   Unit Option.................................................    3
          2.22   Unit Option Price...........................................    3
SECTION   3      ADMINISTRATION..............................................    3
SECTION   4      ELIGIBILITY.................................................    4
SECTION   5      UNITS AVAILABLE FOR THE PLAN................................    4
SECTION   6      UNITS OPTIONS...............................................    5
SECTION   7      UNITS APPRECIATION RIGHTS...................................    8
SECTION   8      RESTRICTED UNITS............................................    9
SECTION   9      REGULATORY APPROVALS AND LISTING............................   10
SECTION  10      EFFECTIVE DATE AND TERM OF PLAN.............................   10
SECTION  11      GENERAL PROVISIONS..........................................   11
SECTION  12      COMPLIANCE WITH RULE 16b-3..................................   12
SECTION  13      AMENDMENT, TERMINATION OR DISCONTINUANCE OF THE PLAN........   12
</TABLE>
 
                                        i
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                     LEVIATHAN GAS PIPELINE PARTNERS, L.P.
 
                         1998 OMNIBUS COMPENSATION PLAN
 
                                   SECTION 1
 
                                    PURPOSES
 
     The purposes of the Leviathan Gas Pipeline Partners, L.P. 1998 Omnibus
Compensation Plan (the "Plan") are to promote the interests of Leviathan Gas
Pipeline Partners, L.P., a Delaware limited partnership (the "Company") and its
unitholders by strengthening its ability to attract and retain officers and key
management employees ("key management employees" means those employees who hold
the position of department director) in the employ of the Company, the General
Partner (as defined below) or their affiliates by furnishing suitable
recognition of their ability and industry which contributed materially to the
success of the Company and to align the interests and efforts of the Company's
and General Partner's officers and key management employees to the long-term
interests of the Company's unitholders. The Plan provides for the grant of unit
options, unit appreciation rights and restricted units in accordance with the
terms and conditions set forth below.
 
                                   SECTION 2
 
                                  DEFINITIONS
 
     Unless otherwise required by the context, the following terms when used in
the Plan shall have the meanings set forth in this Section 2:
 
2.1  BENEFICIARY
 
     The person or persons designated by the Participant pursuant to Section
6.4(f) of this Plan to whom payments are to be paid pursuant to the terms of the
Plan in the event of the Participant's death.
 
2.2  BOARD OF DIRECTORS
 
     The Board of Directors of the General Partner.
 
2.3  CAUSE
 
     The Company may terminate the Participant's employment for Cause. A
termination for Cause is a termination evidenced by a resolution adopted in good
faith by two-thirds (2/3) of the Board of Directors that the Participant (i)
willfully and continually failed to substantially perform the Participant's
duties with the Company (other than a failure resulting from the Participant's
incapacity due to physical or mental illness) which failure continued for a
period of at least thirty (30) days after a written notice of demand for
substantial performance had been delivered to the Participant specifying the
manner in which the Participant has failed to substantially perform or (ii)
willfully engaged in conduct which is demonstrably and materially injurious to
the Company, monetarily or otherwise; provided, however, that no termination of
the Participant's employment shall be for Cause as set forth in clause (ii)
above until (A) there shall have been delivered to the Participant a copy of a
written notice setting forth that the Participant was guilty of the conduct set
forth in clause (ii) above and specifying the particulars thereof in detail and
(B) the Participant shall have been provided an opportunity to be heard by the
Board of Directors (with the assistance of the Participant's counsel if the
Participant so desires). No act, nor failure to act, on the Participant's part
shall be considered "willful" unless the Participant has acted, or failed to
act, with an absence of good faith and without a reasonable belief that the
Participant's action or failure to act was in the best interest of the Company.
Notwithstanding anything contained in the Plan to the contrary, no failure to
perform by the Participant after notice of termination is given by the
Participant shall constitute Cause.
<PAGE>   4
 
2.4  CODE
 
     The Internal Revenue Code of 1986, as amended and in effect from time to
time, and the temporary or final regulations of the Secretary of the U.S.
Treasury adopted pursuant to the Code.
 
2.5  COMMON UNITS
 
     The Common Units of the Company, as defined and described in the Amended
and Restated Agreement of Limited Partnership of the Company, dated February 19,
1993, as amended from time to time.
 
2.6  COMPANY
 
     Leviathan Gas Pipeline Partners, L.P., a Delaware limited partnership, and
any successor in interest.
 
2.7  EXCHANGE ACT
 
     The Securities Exchange Act of 1934, as amended.
 
2.8  FAIR MARKET VALUE
 
     As applied to a specific date, Fair Market Value shall be deemed to be the
mean between the highest and lowest quoted selling prices at which Common Units
are sold on such date as reported in the New York Stock Exchange
("NYSE")-Composite Transactions by The Wall Street Journal on such date, or if
no Common Units were traded on such date, on the next preceding day on which
Common Units were so traded.
 
2.9  GENERAL PARTNER
 
     General Partner means Leviathan Gas Pipeline Company, a Delaware
corporation and the general partner of the Company.
 
2.10  MANAGEMENT COMMITTEE
 
     A committee consisting of the Chairman of the Board of the General Partner
and such other senior officers as the Chairman of the Board shall designate.
 
2.11  MAXIMUM ANNUAL EMPLOYEE GRANT
 
     The Maximum Annual Employee Grant set forth in Section 5.3.
 
2.12  PARTICIPANT
 
     An eligible employee to whom a unit option, unit appreciation right or
Restricted Unit is granted under the Plan as set forth in Section 4.
 
2.13  PERFORMANCE GOALS
 
     The Plan Administrator shall establish one or more performance goals
("Performance Goals") for each Performance Period in writing. Such Performance
Goals shall be set no later than the commencement of the applicable Performance
Period, or such later date as may be permitted with respect to
"performance-based" compensation under Section 162(m) of the Code.
 
2.14  PERFORMANCE PERIOD
 
     That period of time during which Performance Goals are measured to
determine the vesting or granting of unit options, unit appreciation rights or
Restricted Units, as the Plan Administrator may determine.
 
                                        2
<PAGE>   5
 
2.15  PERMANENT DISABILITY OR PERMANENTLY DISABLED
 
     A Participant shall be deemed to have become Permanently Disabled for
purposes of the Plan if the Chairman of the Board of the General Partner shall
find upon the basis of medical evidence satisfactory to the Chairman of the
Board that the Participant is totally disabled, whether due to physical or
mental condition, so as to be prevented from engaging in further employment by
the Company, the General Partner or any of their affiliate, and that such
disability will be permanent and continuous during the remainder of the
Participant's life; provided, that with respect to Section 16 Insiders such
determination shall be made by the Plan Administrator.
 
2.16  PLAN ADMINISTRATOR
 
     The Compensation Committee of the Board of Directors of the General Partner
or any other committee appointed and/or authorized pursuant to Section 3 to
administer the Plan, including the Management Committee.
 
2.17  RESTRICTED UNITS
 
     Common Units granted under the Plan that are subject to the requirements of
Section 8 and such other restrictions as the Plan Administrator deems
appropriate. References to Restricted Units in this Plan shall include
Performance Restricted Units (as defined in Section 5.2) unless the context
otherwise requires.
 
2.18  RULE 16B-3
 
     Rule 16b-3 of the General Rules and Regulations under the Exchange Act.
 
2.19  SECTION 16 INSIDER
 
     Any person who is selected by the Plan Administrator to receive unit
options, unit appreciation rights or Restricted Units pursuant to the Plan and
who is subject to the requirements of Section 16 of the Exchange Act, and the
rules and regulations promulgated thereunder.
 
2.21  UNIT OPTION
 
     An option to acquire a Common Unit of the Company at the unit option price,
and which is not intended to meet the requirements of an incentive option as
defined in Section 422 of the Code.
 
2.22  UNIT OPTION PRICE
 
     The price at which each unit option is exercisable for a Common Unit.
 
                                   SECTION 3
 
                                 ADMINISTRATION
 
     3.1  With respect to awards made under the Plan to Section 16 Insiders, the
Plan shall be administered by the Compensation Committee of the General
Partner's Board of Directors, which shall be constituted at all times so awards
to Section 16 Insiders pursuant to this Plan shall qualify as an exception to
liability under Section 16(b) of the Exchange Act, so long as any of the
Company's equity securities are registered pursuant to Section 12(b) or 12(g) of
the Exchange Act. Except as provided below, and as may be required by Section
16(b) of the Exchange Act, the Plan shall be administered by the Management
Committee. The Management Committee shall interpret the Plan, prescribe, amend,
and rescind rules relating to it, select eligible Participants, make grants to
Participants who are not Section 16 Insiders, and take all other actions
necessary for its administration, which actions shall be final and binding upon
all Participants.
 
     3.2  Except for the terms and conditions explicitly set forth in the Plan,
the Management Committee shall have sole authority to construe and interpret the
Plan, to establish, amend and rescind rules and
 
                                        3
<PAGE>   6
 
regulations relating to the Plan, to select persons eligible to participate in
the Plan, to grant unit options, unit appreciation rights and Restricted Units
thereunder, to administer the Plan, to make recommendations to the Board of
Directors, and to take all such steps and make all such determinations in
connection with the Plan and the unit options, unit appreciation rights and
Restricted Units granted thereunder as it may deem necessary or advisable, which
determination shall be final and binding upon all Participants. The Plan
Administrator shall cause the Company at its expense to take any action related
to the Plan which may be necessary to comply with the provisions of any federal
or state law or any regulations issued thereunder.
 
     3.3  Each member of any committee acting as Plan Administrator, while
serving as such, shall be considered to be acting in his or her capacity as a
director of the General Partner. Members of the Board of Directors and members
of any committee acting under the Plan shall be fully protected in relying in
good faith upon the advice of counsel and shall incur no liability except for
gross negligence or willful misconduct in the performance of their duties.
 
                                   SECTION 4
 
                                  ELIGIBILITY
 
     To be eligible for selection by the Plan Administrator to participate in
the Plan, an individual must be an officer or key management employee of the
Company, the General Partner, or any their affiliates, as of the date on which
the Plan Administrator grants to such individual a unit option, unit
appreciation right or Restricted Units or a person who, in the judgment of the
Plan Administrator, holds a position of responsibility and is able to contribute
substantially to the Company's continued success. Members of the Board of
Directors of the General Partner who are full-time salaried officers shall be
eligible to participate. Members of the Board of Directors who are not employees
are not eligible to participate in this Plan.
 
                                   SECTION 5
 
                          UNITS AVAILABLE FOR THE PLAN
 
     5.1  Subject to Section 5.4, the maximum number of units that may be issued
for which unit options, unit appreciation rights and Restricted Units may at any
time be granted under the Plan is three million (3,000,000) Common Units, from
units held in the Company's treasury or out of the authorized but unissued units
of the Company, or the General Partner, as appropriate, or partly out of each,
as shall be determined by the Plan Administrator.
 
     5.2  Notwithstanding the foregoing, and subject to Section 5.4, the number
of units for which Restricted Units may be granted pursuant to Section 8 of the
Plan may not exceed five hundred thousand (500,000) Common Units, unless the
granting or vesting of such Restricted Units is in compliance with the
performance-based requirements of Section 162(m) of the Code ("Performance
Restricted Units"). The grant of Performance Restricted Units is not limited by
this Section 5.2.
 
     5.3  The maximum number of units with respect to which awards under this
Plan may be granted to any eligible employee in any one year shall not exceed:
(a) five hundred thousand (500,000) in the case of unit options (and unit
appreciation rights) and (b) five hundred thousand (500,000) in the case of
Restricted Units (whether or not such Restricted Units are Performance
Restricted Units). The foregoing maximums shall be referred to collectively as
the "Maximum Annual Employee Grant."
 
     5.4  In the event of a recapitalization, unit split, unit dividend,
exchange of units, merger, reorganization, change in corporate structure or
units of the Company or similar event, the Board of Directors, upon the
recommendation of the Plan Administrator, may make appropriate adjustments in
the number of units authorized for the Plan, the Maximum Annual Employee Grant
and, with respect to outstanding unit options, unit appreciation rights and
Restricted Units, the Plan Administrator may make appropriate adjustments in the
number of units and the Unit Option Price.
 
                                        4
<PAGE>   7
 
                                   SECTION 6
 
                                  UNIT OPTIONS
 
     6.1  Unit options may be granted to eligible employees in such number, and
at such times during the term of the Plan as the Plan Administrator shall
determine, the Plan Administrator taking into account the duties of the
respective employees, their present and potential contributions to the success
of the Company, and such other factors as the Plan Administrator shall deem
relevant in accomplishing the purposes of the Plan. The granting of a unit
option shall take place when the Plan Administrator by resolution, written
consent or other appropriate action determines to grant such a unit option to a
particular Participant at a particular price. Each unit option shall be
evidenced by a written instrument delivered by or on behalf of the Company
containing provisions not inconsistent with the Plan.
 
     6.2  All unit options under the Plan shall be granted subject to the
following terms and conditions:
 
     (a) Unit Option Price
 
          The Unit Option Price shall be determined by the Plan Administrator,
     but shall not be less than one hundred percent (100%) of the Fair Market
     Value of the Common Units on the date the unit option is granted.
 
     (b) Duration of Unit Options
 
          Unit options shall be exercisable at such time and under such
     conditions as set forth in the unit option grant, but in no event shall any
     unit option be exercisable later than the tenth anniversary of the date of
     its grant.
 
     (c) Exercise of Unit Options
 
          Unless otherwise provided by the Plan Administrator, a Participant may
     not exercise a unit option until the Participant has completed one (1) year
     of continuous employment with the Company, the General Partner or any of
     their affiliates from and including the date on which the unit option is
     granted. This requirement is waived in the event of death or Permanent
     Disability of a Participant before such period of continuous employment is
     completed and may be waived or modified in the agreement evidencing the
     option or by resolution adopted at any time by the Plan Administrator.
     Thereafter, Common Units covered by a unit option may be purchased at one
     time or in such installments over the balance of the unit option period as
     may be provided in the unit option grant. Any units not purchased on the
     applicable installment date may be purchased thereafter at any time prior
     to the final expiration of the unit option. To the extent that the right to
     purchase units has accrued thereunder, unit options may be exercised from
     time to time by written notice to the Company or General Partner, as
     appropriate, setting forth the number of units with respect to which the
     unit option is being exercised, and such additional information as may be
     required by the Plan Administrator.
 
     (d) Payment
 
          The purchase price of units purchased under unit options shall be paid
     in full to the Company upon the exercise of the unit option by delivery of
     consideration equal to the product of the Option Price and the number of
     units purchased (the "Purchase Price"). Such consideration may be either
     (i) in cash or (ii) at the discretion of the Plan Administrator, in Common
     Units already owned by the Participant for at sufficient time (generally
     six (6) months) to not result in an accounting charge to the Company, or
     any combination of cash and Common Units. The Fair Market Value of such
     Common Units as delivered shall be valued as of the day prior to delivery.
     The Plan Administrator can determine at the time the unit option is granted
     that additional forms of payment will be permitted. To the extent permitted
     by the Plan Administrator and applicable laws and regulations (including,
     but not limited to, federal tax and securities laws, regulations and state
     corporate law), an option may also be exercised by delivery of a properly
     executed exercise notice together with irrevocable instructions to a broker
     to promptly deliver to the Company the amount of sale or loan proceeds to
     pay the Purchase Price. A Participant shall have none of the rights of a
     unit holder until the units of Common Units are issued to the Participant.
 
                                        5
<PAGE>   8
 
          If specifically authorized in the unit option grant, a Participant may
     elect to pay all or a portion of the Purchase Price by having Common Units
     with a Fair Market Value equal to all or a portion of the Purchase Price be
     withheld from the units issuable to the Participant upon the exercise of
     the unit option. The Fair Market Value of such Common Units as is withheld
     shall be determined as of the same day as the exercise of the unit option.
     In the event a unit option grant to a Section 16 Insider provides that the
     Purchase Price may be paid in whole or in part by having units with a Fair
     Market Value equal to all or a portion of the Purchase Price withheld from
     the units issuable to the Participant upon the exercise of the unit option,
     the withholding of units issuable upon the exercise of a unit option to pay
     the Purchase Price by a Section 16 Insider must be in accordance with
     applicable requirements of an exemption to liability under Section 16(b) or
     the rules promulgated thereunder.
 
     (e) Restrictions
 
          The Plan Administrator shall determine and reflect in the unit option
     grant, with respect to each unit option, the nature and extent of the
     restrictions, if any, to be imposed on the units of Common Units which may
     be purchased thereunder, including, but not limited to, restrictions on the
     transferability of such units acquired through the exercise of such unit
     options for such periods as the Plan Administrator may determine and,
     further, that in the event a Participant's employment by the Company, the
     General Partner or any of their affiliates, terminates during the period in
     which such units are nontransferable, the Participant shall be required to
     sell such units back to the Company at such prices as the Plan
     Administrator may specify in the unit option.
 
     (f) Nontransferability of Unit Options
 
          During a Participant's lifetime, a unit option may be exercisable only
     by the Participant. Unit options granted under the Plan and the rights and
     privileges conferred thereby shall not be subject to execution, attachment
     or similar process and may not be transferred, assigned, pledged or
     hypothecated in any manner (whether by operation of law or otherwise) other
     than by will or by the applicable laws of descent and distribution.
     Notwithstanding the foregoing, to the extent permitted by applicable law,
     the Plan Administrator may permit a recipient of a unit option to designate
     in writing during the Participant's lifetime a Beneficiary to receive and
     exercise the Participant's unit options in the event of such Participant's
     death (as provided in Section 6.2(i)). If any Participant attempts to
     transfer, assign, pledge, hypothecate or otherwise dispose of any option
     under the Plan or of any right or privilege conferred thereby, contrary to
     the provisions of the Plan, or suffers the sale or levy or any attachment
     or similar process upon the rights and privileges conferred hereby, all
     affected unit options held by such Participant shall be immediately
     forfeited.
 
     (g) Purchase for Investment
 
          The Plan Administrator shall have the right to require that each
     Participant or other person who shall exercise a unit option under the
     Plan, and each person into whose name Common Units shall be issued pursuant
     to the exercise of a unit option, represent and agree that any and all
     Common Units purchased pursuant to such unit option are being purchased for
     investment only and not with a view to the distribution or resale thereof
     and that such units will not be sold except in accordance with such
     restrictions or limitations as may be set forth in the unit option. This
     Section 6.2(g) shall be inoperative during any period of time when the
     Company has obtained all necessary or advisable approvals from governmental
     agencies and has completed all necessary or advisable registrations or
     other qualifications of Common Units as to which unit options may from time
     to time be granted as contemplated in Section 9.
 
     (h) Termination of Employment
 
          Upon the termination of a Participant's employment for any reason
     other than death or Permanent Disability, the Participant's unit option
     shall be exercisable only to the extent that it was then exercisable and,
     unless the term of the unit options expires sooner, such unit options shall
     expire according to the following schedule; provided, that the Plan
     Administrator may at any time determine in a particular case
 
                                        6
<PAGE>   9
 
     that specific limitations and restrictions under the Plan shall not apply,
     or that a unit option should expire sooner or should terminate when the
     Participant's employment status ceases:
 
        (i) Retirement
 
             The unit option shall expire, unless exercised, thirty-six (36)
        months after the Participant's retirement from the Company, the General
        Partner or any of their affiliates.
 
        (ii) Disability
 
             The unit option shall expire, unless exercised, thirty-six (36)
        months after the Participant's Permanent Disability.
 
          (iii) Termination
 
             Subject to subparagraph (iv) below, the unit option shall expire,
        unless exercised, three (3) months after a Participant resigns or is
        terminated as an employee of the Company, the General Partner or any of
        their affiliates, other than for Cause, unless the Chairman of the Board
        of the General Partner shall have determined in a specific case that the
        unit option should expire sooner or should terminate when the
        Participant's employment status ceases; provided, however, that for
        Section 16 Insiders, such determination shall be made by the Plan
        Administrator.
 
          (iv) All Other Terminations
 
             Notwithstanding subparagraphs (iii) and (iv) above, the unit option
        shall expire upon termination of employment for Cause, unless exercised,
        one year after the Participant's termination of employment on account of
        disability (as defined in Section 22(e)(3) of the Code) and shall expire
        three (3) months after the Participant's termination of employment other
        than on account of death, Permanent Disability or termination for Cause.
 
     (i) Death of Participant
 
          Upon the death of a Participant, whether during the Participant's
     period of employment or during the thirty-six (36) month period referred to
     in Sections 6.2(h)(i), (ii) and (iii), the unit option shall expire, unless
     the original term of the unit option expires sooner, twelve (12) months
     after the date of the Participant's death, unless the unit option is
     exercised within such twelve (12) month period by the Participant's
     Beneficiary, legal representatives, estate or the person or persons to whom
     the deceased's unit option rights shall have passed by will or the laws of
     descent and distribution; provided, that the Plan Administrator shall
     determine in a particular case that specific limitations and restrictions
     under the Plan shall not apply. Notwithstanding any other Plan provisions
     pertaining to the times at which unit options may be exercised, no unit
     option shall continue to be exercisable, pursuant to Section 6.2(h) or this
     Section 6.2(i), at a time that would violate the maximum duration of
     Section 6.2(b).
 
     (j) Deferral Election
 
          A Participant may elect irrevocably (at a time and in a manner
     determined by the Plan Administrator) prior to exercising a unit option
     granted under the Plan that issuance of Common Units upon exercise of such
     unit option shall be deferred until a pre-specified date in the future or
     until the Participant ceases to be employed by the Company or any of its
     Subsidiaries, as elected by the Participant. After the exercise of any such
     unit option and prior to the issuance of any deferred units, the number of
     Common Units issuable to the Participant shall be credited to a memorandum
     deferred account and any dividends or other distributions paid on the
     Common Units shall be deemed reinvested in additional Common Units until
     all credited units shall become issuable pursuant to the Participant's
     election.
 
                                        7
<PAGE>   10
 
                                   SECTION 7
 
                            UNIT APPRECIATION RIGHTS
 
     7.1  The Plan Administrator may grant unit appreciation rights to
Participants in connection with any unit option granted under the Plan, either
at the time of the grant of such unit option or at any time thereafter during
the term of the unit option. Such unit appreciation rights shall cover the same
units covered by the unit options (or such lesser number of Common Units as the
Plan Administrator may determine) and shall, except as provided in Section 7.3,
be subject to the same terms and conditions as the related unit options and such
further terms and conditions not inconsistent with the Plan as shall from time
to time be determined by the Plan Administrator.
 
     7.2  Each unit appreciation right shall entitle the holder of the related
unit option to surrender to the Company unexercised the related unit option, or
any portion thereof, and to receive from the Company in exchange therefor an
amount equal to the excess of the Fair Market Value of one Common Unit on the
date the right is exercised over the Option Price per share times the number of
units covered by the unit option, or portion thereof, which is surrendered.
Payment shall be made in Common Units valued at Fair Market Value as of the date
the right is exercised, or in cash, or partly in units and partly in cash, at
the discretion of the Plan Administrator. Notwithstanding the foregoing and to
the extent required by an applicable exemption to liability under Section 16(b),
a payment, in whole or in part, of cash upon exercise of a unit appreciation
right by a Section 16 Insider may be made only if the Plan Administrator
approves such election to receive cash and the right is exercised in accordance
with the requirements of such exemption under Section 16(b). Unit appreciation
rights may be exercised from time to time upon actual receipt by the Company of
written notice stating the number of Common Units with respect to which the unit
appreciation right is being exercised. The value of any fractional units shall
be paid in cash.
 
     7.3  Unit appreciation rights are subject to the following restrictions:
 
          (a) Each unit appreciation right shall be exercisable at such time or
     times as the unit option to which it relates shall be exercisable, or at
     such other times as the Plan Administrator may determine; provided,
     however, that such right shall not be exercisable until the Participant
     shall have completed a six (6) month period of continuous employment with
     the Company or any of its Subsidiaries immediately following the date on
     which the unit appreciation right is granted. In the event of death or
     Permanent Disability of a Participant during employment but before the
     Participant has completed such period of continuous employment, such unit
     appreciation right shall be exercisable; but only within the period
     specified in the related unit option. Notwithstanding the foregoing, a unit
     appreciation right may not be exercised for cash by a Section 16 Insider
     unless such exercise is pursuant to an exemption to liability under Section
     16(b) or rules promulgated thereunder.
 
          (b) The Plan Administrator in its sole discretion may approve or deny
     in whole or in part a request to exercise a unit appreciation right. Denial
     or approval of such request shall not require a subsequent request to be
     similarly treated by the Plan Administrator.
 
          (c) The right of a Participant to exercise a unit appreciation right
     shall be canceled if and to the extent the related unit option is
     exercised. To the extent that a unit appreciation right is exercised, the
     related unit option shall be deemed to have been surrendered unexercised
     and canceled.
 
          (d) A holder of unit appreciation rights shall have none of the rights
     of a units holder until Common Units, if any, are issued to such holder
     pursuant to such holder's exercise of such rights.
 
          (e) The acquisition of Common Units pursuant to the exercise of a unit
     appreciation right shall be subject to the same restrictions as would apply
     to the acquisition of Common Units acquired upon acquisition of the related
     unit option, as set forth in Section 6.2.
 
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<PAGE>   11
 
                                   SECTION 8
 
                                RESTRICTED UNITS
 
     8.1  Subject to Sections 5.2 and 5.3, Restricted Units (including
Performance Restricted Units as described in Section 8.2 below) may be granted
to Participants in such number and at such times during the term of the Plan as
the Plan Administrator shall determine, taking into account the duties of the
respective Participants, their present and potential contributions to the
success of the Company, and such other factors as the Plan Administrator shall
deem relevant in accomplishing the purposes of the Plan. The granting of
Restricted Units shall take place when the Plan Administrator by resolution,
written consent or other appropriate action determines to grant such Restricted
Units to a particular Participant. Each grant shall be evidenced by a written
instrument delivered by or on behalf of the Company containing provisions not
inconsistent with the Plan. The Participant receiving a grant of Restricted
Units shall be recorded as a unitholder of the Company. Each Participant who
receives a grant of Restricted Units shall have all the rights of a unit holder
with respect to such units (except as provided in the restrictions on
transferability), including, but not limited to, the right to distributions on
such Common Units; provided, however, that no Participant awarded Restricted
Units shall have any right as a unit holder with respect to any units subject to
the Participant's Restricted Units grant prior to the date of issuance to the
Participant of a certificate or certificates for such units.
 
     8.2  Notwithstanding any other provision to the contrary in this Section 8,
before Performance Restricted Units can be granted or vested, as applicable, the
Plan Administrator shall:
 
          (a) Determine the Performance Goals applicable to the particular
     Performance Period; and
 
          (b) Certify in writing that such Performance Goals for a particular
     Performance Period have been attained.
 
     8.3  A grant of Restricted Units shall entitle a Participant to receive, on
the date or dates designated by the Plan Administrator, upon payment to the
Company of the par value, if applicable, of the Common Units in a manner
determined by the Plan Administrator, the number of Common Units selected by the
Plan Administrator. The Plan Administrator may require, under such terms and
conditions as it deems appropriate or desirable, that the certificates (if
issued) for Restricted Units delivered under the Plan may be held in custody by
a bank or other institution, or that the Company may itself hold such units in
custody until the Restriction Period (as defined in Section 8.4) expires or
until restrictions thereon otherwise lapse, and may require, as a condition of
any issuance of Restricted Units that the Participant shall have delivered a
units power endorsed in blank relating to the Restricted Units.
 
     8.4  During a period of years following the date of grant, as determined by
the Plan Administrator, which shall in no event be less than one (1) year (the
"Restriction Period"), the Restricted Units may not be sold, assigned,
transferred, pledged, hypothecated or otherwise encumbered or disposed of by the
recipient, except in the event of death or Permanent Disability, the transfer to
the Company as provided under the Plan or the Plan Administrator's waiver or
modification of such restrictions in the agreement evidencing the grant of
Restricted Units, or by resolution of the Plan Administrator adopted at any
time.
 
     8.5  Except as provided in Section 8.6, if a Participant terminates
employment with the Company for any reason before the expiration of the
Restriction Period, all Restricted Units still subject to restriction shall be
forfeited by the Participant to the Company. In addition, in the event of any
attempt by the Participant to sell, exchange, transfer, pledge or otherwise
dispose of Restricted Units in violation of the terms of the Plan, such units
shall be forfeited to the Company.
 
     8.6  The Restriction Period for any Participant shall be deemed to end and
all restrictions on Restricted Units shall lapse, upon the Participant's death
or Permanent Disability or any termination of employment determined by the Plan
Administrator to end the Restriction Period.
 
     8.7  When the restrictions imposed by Section 8.4 expire or otherwise lapse
with respect to one or more Restricted Units, the Company shall deliver to the
Participant (or the Participant's legal representative,
 
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<PAGE>   12
 
Beneficiary or heir) one (1) Common Unit for each Restricted Unit. At that time,
the agreement referred to in Section 8.1, as it relates to such units, shall be
terminated.
 
     8.8  Subject to Section 8.3 (and Section 8.2 in the case of Performance
Restricted Units), a Participant entitled to receive Restricted Units under the
Plan shall be issued a certificate or shall have a book entry account
established for such units. Such certificate or account shall be registered in
the name of the Participant, and shall bear an appropriate legend reciting the
terms, conditions and restrictions, if any, applicable to such units and shall
be subject to appropriate stop-transfer orders.
 
                                   SECTION 9
 
                        REGULATORY APPROVALS AND LISTING
 
     9.1  The Company shall not be required to issue any certificate or
establish any account for Common Units upon the exercise of a unit option or a
unit appreciation right granted under the Plan, with respect to a grant of
Restricted Units or Common Units awarded as payment of vested units prior to:
 
          (a) obtaining any approval or ruling from the Securities and Exchange
     Commission, the Internal Revenue Service or any other governmental agency
     which the Company or the General Partner, in its sole discretion, shall
     determine to be necessary or advisable;
 
          (b) listing of such units on any stock exchange on which the Common
     Units may then be listed; or
 
          (c) completing any registration or other qualification of such units
     under any federal or state laws, rulings or regulations of any governmental
     body which the Company or the General Partner, in its sole discretion,
     shall determine to be necessary or advisable.
 
     All certificates or accounts for Common Units delivered under the Plan
shall also be subject to such stop-transfer orders and other restrictions as the
Plan Administrator may deem advisable under the rules, regulations and other
requirements of the Securities and Exchange Commission, any stock exchange upon
which Common Units is then listed and any applicable federal or State securities
laws, and the Plan Administrator may cause a legend or legends to be placed on
any such certificates or accounts to make appropriate reference to such
restrictions. The foregoing provisions of this paragraph shall not be effective
if and to the extent that the Common Units delivered under the Plan are covered
by an effective and current registration statement under the Securities Act of
1933, as amended, or if and so long as the Plan Administrator determines that
application of such provisions is no longer required or desirable. In making
such determination, the Plan Administrator may rely upon an opinion of counsel
for the Company or the General Partner.
 
                                   SECTION 10
 
                        EFFECTIVE DATE AND TERM OF PLAN
 
     The Plan shall be effective as of August 14, 1998, and shall terminate ten
(10) years therefrom, unless terminated earlier pursuant to Section 13, herein.
Unit options, unit appreciation rights and Restricted Units theretofore granted
may extend beyond that date and the terms and conditions of the Plan shall
continue to apply thereto and to Common Units acquired thereunder. To the extent
required for compliance with Section 16(b) and rules promulgated thereunder,
Common Units underlying unit options, unit appreciation rights and Restricted
Units granted to Section 16 Insiders may not be sold until a date at least six
(6) months after the date such General Partner approval of the Plan is obtained,
and unit appreciation rights that are granted subject to General Partner
approval of the Plan to Section 16 Insiders may not be exercised for cash until
a date at least six (6) months after the date such General Partner approval is
obtained.
 
                                       10
<PAGE>   13
 
                                   SECTION 11
 
                               GENERAL PROVISIONS
 
     11.1  Nothing contained in the Plan, or in any unit option, unit
appreciation right or Restricted Unit granted pursuant to the Plan, shall confer
upon any employee any right with respect to continuance of employment by the
Company, the General Partner or any of their affiliates, nor interfere in any
way with the right of the Company, the General Partner or any of their
affiliates to terminate the employment of such employee at any time with or
without assigning any reason therefor.
 
     11.2  Grants, vesting or payment of unit options, unit appreciation rights
or Restricted Units shall not be considered as part of a Participant's salary or
used for the calculation of any other pay, allowance, pension or other benefit
unless otherwise permitted by other benefit plans provided by the Company, the
General Partner or any of their affiliates, or required by law or by contractual
obligations of the Company, the General Partner or any of their affiliates.
 
     11.3  The right of a Participant or Beneficiary to the payment of any
compensation under the Plan may not be assigned, transferred, pledged or
encumbered, nor shall such right or other interests be subject to attachment,
garnishment, execution or other legal process.
 
     11.4  Leaves of absence for such periods and purposes conforming to the
personnel policy of the Company, the General Partner or any of their affiliates,
as applicable, shall not be deemed terminations or interruptions of employment,
unless a Participant commences a leave of absence from which he or she is not
expected to return to active employment with the Company, the General Partner or
any of their affiliates.
 
     11.5  In the event a Participant is transferred from the Company to the
General Partner or other affiliate, or vice versa, or is promoted or given
different responsibilities, the unit options, unit appreciation rights and
Restricted Units granted to the Participant prior to such date shall not be
affected.
 
     11.6  The Plan shall be construed and governed in accordance with the laws
of the State of Texas, except that it shall be construed and governed in
accordance with applicable federal law in the event that such federal law
preempts state law.
 
     11.7  Appropriate provision shall be made for all taxes required to be
withheld in connection with the exercise, grant or other taxable event with
respect to unit option, unit appreciation rights and Restricted Units under the
applicable laws or regulations of any governmental authority, whether federal,
state or local and whether domestic or foreign, including, but not limited to,
the required withholding of a sufficient number of units otherwise issuable to a
Participant to satisfy the said required minimum tax withholding obligations. If
provided in the grant, a Participant is permitted to deliver Common Units
(including units acquired pursuant to the exercise of a unit option or unit
appreciation right other than the unit option or unit appreciation right
currently being exercised, to the extent permitted by applicable regulations)
for payment of withholding taxes on the exercise of a unit option or unit
appreciation right, or upon the grant or vesting of Restricted Units. At the
election of the Plan Administrator or, subject to approval of the Plan
Administrator at its sole discretion, at the election of a Participant, Common
Units may be withheld from the units issuable to the Participant upon the
exercise of a unit option or unit appreciation right or upon the vesting of the
Restricted Units to satisfy tax withholding obligations. The Fair Market Value
of Common Units as delivered pursuant to this Section 11.7 shall be valued as of
the day prior to delivery, and shall be calculated in accordance with Section
2.8. The election by a Section 16 Insider to have Common Units withheld to pay
tax obligations in connection with the exercise of a unit option or unit
appreciation right or the vesting of Restricted Units must be made in accordance
with the provisions, if any, of Section 16 and the rules promulgated thereunder.
 
     Any Participant that makes a Section 83(b) election under the Code shall,
within ten (10) days of making such election, notify the Company in writing of
such election and shall provide the Company with a copy of such election form
filed with the Internal Revenue Service.
 
     Tax advice should be obtained by the Participant prior to the Participant's
(i) entering into any transaction under or with respect to the Plan, (ii)
designating or choosing the times of distributions under the Plan, or (iii)
disposing of any Common Units issued under the Plan.
                                       11
<PAGE>   14
 
                                   SECTION 12
 
                           COMPLIANCE WITH SECTION 16
 
     The Company's intention is that, so long as any of the Company's equity
securities are registered pursuant to Section 12(b) or 12(g) of the Exchange
Act, with respect to awards granted to or held by Section 16 Insiders, the Plan
shall comply in all respects with Rule 16b-3 or any successor rule or rule of
similar application under Section 16 of the Exchange Act or rules thereunder. If
any Plan provision is later found not to be in compliance with Rule 16b-3 or
such other rules promulgated under Section 16 of the Exchange Act, that
provision shall be deemed modified as necessary to meet the requirements of
Section 16.
 
     Notwithstanding anything in the Plan to the contrary, the Board, in its
absolute discretion, may bifurcate the Plan so as to restrict, limit, or
condition the applicability of any provision of the Plan to Participants who are
Section 16 Insiders without so restricting, limiting, or conditioning the Plan
with respect to other Participants.
 
                                   SECTION 13
 
              AMENDMENT, TERMINATION OR DISCONTINUANCE OF THE PLAN
 
     13.1  Subject to the Board of Directors of the General Partner and Section
13.2, the Plan Administrator may from time to time make such amendments to the
Plan as it may deem proper and in the best interest of the Company without
further approval of the General Partner of the Company, including, but not
limited to, any amendment necessary to ensure that the Company may obtain any
regulatory approval referred to in Section 11; provided, however, that no change
in any unit option, unit appreciation right or Restricted Units theretofore
granted may be made without the consent of the Participant which would impair
the right of the Participant to acquire or retain Common Units or cash that the
Participant may have acquired as a result of the Plan.
 
     13.2  To the extent required for compliance with applicable law or
regulation, including Section 16(b), the Plan Administrator and the Board of
Directors may not amend the Plan without the approval of the sole stockholder of
the General Partner to:
 
          (a) materially increase the number of units or rights that may be
     issued under the Plan to Section 16 Insiders;
 
          (b) otherwise materially increase the benefits accruing to the
     Participants under the Plan.
 
     13.4  The Board of Directors of the General Partner may at any time suspend
the operation of or terminate the Plan with respect to any Common Units or
rights which are not at that time subject to unit option, unit appreciation
right or grant of Restricted Units, not yet granted.
 
                                       12
<PAGE>   15
     IN WITNESS WHEREOF, the Company has caused the Plan to be executed
effective as of August 14, 1998.


 
                                          LEVIATHAN GAS PIPELINE COMPANY,
                                          General Partner
 
                                          By       /s/ H. BRENT AUSTIN
                                            ------------------------------------
                                            Title: Executive Vice President
 
ATTEST:
 
By       /s/ DAVID L. SIDDALL
    ----------------------------------
    Title: Corporate Secretary
 


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