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                                                                    EXHIBIT 10.2
 
                                   LEVIATHAN
                           1998 UNIT OPTION PLAN FOR
                             NON-EMPLOYEE DIRECTORS
 
                        EFFECTIVE AS OF AUGUST 14, 1998
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                               TABLE OF CONTENTS
 
<TABLE>
<S>        <C>                                                            <C>
SECTION 1  PURPOSE.....................................................     1
SECTION 2  UNITS SUBJECT TO THE PLAN...................................     1
SECTION 3  ADMINISTRATION OF THE PLAN..................................     1
SECTION 4  PARTICIPATION IN THE PLAN...................................     1
SECTION 5  UNIT OPTION GRANTS AND TERMS................................     2
SECTION 6  GENERAL PROVISIONS..........................................     3
SECTION 7  EFFECTIVE DATE AND DURATION OF PLAN.........................     4
SECTION 8  COMPLIANCE WITH SECTION 16..................................     4
SECTION 9  AMENDMENT, TERMINATION OR DISCONTINUANCE OF THE PLAN........     4
</TABLE>
<PAGE>   3
 
                                   LEVIATHAN
 
                             1998 UNIT OPTION PLAN
                           FOR NON-EMPLOYEE DIRECTORS
 
                                   SECTION 1
 
                                    PURPOSE
 
     The purpose of the Leviathan 1998 Unit Option Plan for Non-Employee
Directors (the "Plan") is to attract and retain the services of experienced and
knowledgeable non-employee Directors of Leviathan Gas Pipeline Company (the
"Company"), the general partner of Leviathan Gas Pipeline Partners, L.P. (the
"Partnership"), and to provide an incentive for such Directors to increase their
proprietary interests in the Partnership's long-term success and progress.
 
                                   SECTION 2
 
                           UNITS SUBJECT TO THE PLAN
 
     2.1  Subject to Section 2.2, the maximum number of common units of the
Partnership (the "Common Units"), for which unit options may be granted under
the Plan is one hundred thousand (100,000) (the "Units"). The Units shall be
Common Units held in the Company's or the Partnership's, as appropriate,
treasury or issued out of the authorized but unissued units of the Partnership,
or partly out of each, as shall be determined by the Plan Administrator.
 
     2.2  In the event of a recapitalization, unit split, unit dividend,
exchange of shares or units, merger, reorganization, change in corporate
structure or units of the Partnership or similar event, the Board of Directors
of the Company (the "Board"), may make appropriate adjustments in the number of
units authorized for the Plan and, with respect to outstanding unit options, the
Plan Administrator may make appropriate adjustments in the number of units and
the unit option price. In the event of any adjustment in the number of Units
covered by any unit option, any fractional units resulting from such adjustment
shall be disregarded and each such unit option shall cover only the number of
full units resulting from such adjustment.
 
                                   SECTION 3
 
                           ADMINISTRATION OF THE PLAN
 
     Unless otherwise determined by the Board and subject to Section 9, the Plan
shall be administered by a management committee (the "Plan Administrator")
consisting of the Chairman of the Board of the Company and such other senior
officers of the Company or its affiliates as the Chairman of the Board shall
designate. The Plan Administrator shall interpret the Plan, shall prescribe,
amend and rescind rules relating to it from time to time as it deems proper and
in the best interests of the Company and the Partnership, and shall take any
other action necessary for the administration of the Plan.
 
                                   SECTION 4
 
                           PARTICIPATION IN THE PLAN
 
     Each member of the Board elected or appointed who is not otherwise an
employee of the Company, the Partnership or any subsidiary thereof (a
"Participant") shall receive unit option grants as provided in the Plan.
<PAGE>   4
 
                                   SECTION 5
 
                          UNIT OPTION GRANTS AND TERMS
 
     Each unit option granted to a Participant under the Plan and the issuance
of Units thereunder shall be subject to the following terms:
 
5.1  UNIT OPTION GRANTS
 
     A Participant shall automatically receive (a) a grant of unit options to
purchase one thousand five hundred (1,500) Units when the Participant is
initially elected or appointed as a Director of the Company and (b) a grant of
unit options to purchase one thousand (1,000) Units on each date the Participant
is reelected as a Director of the Company at the Annual Meeting of Stockholders
of the Company (the "Annual Meeting"), beginning with the Annual Meeting in
1999.
 
     Each option granted under the Plan shall be evidenced by a written
instrument delivered by or on behalf of the Plan Administrator containing terms,
provisions and conditions not inconsistent with the Plan.
 
5.2  VESTING OF UNIT OPTIONS
 
     Each unit option granted to a Participant under the Plan shall be fully
vested and immediately exercisable upon grant.
 
5.3  UNIT OPTION PRICE
 
     The unit option price for a unit option granted under the Plan shall be the
fair market value of the Units covered by the unit option at the time the unit
option is granted. For purposes of the Plan, "fair market value" shall be the
mean between the highest and lowest quoted selling prices at which the Common
Units were sold on such date as reported in the 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 date on which Common Units were so traded.
 
5.4  TIME AND MANNER OF EXERCISE OF A UNIT OPTION
 
     Each unit option may be exercised in whole or in part at any time and from
time to time; provided, however, that no fewer than one hundred (100) Units (or
the remaining Units then purchasable under the unit option, if less than one
hundred (100) Units) may be purchased upon exercise of any unit option hereunder
and that only whole Units will be issued pursuant to the exercise of any unit
option.
 
     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 unit option price and the number of
units purchased (the "Purchase Price"). Such consideration may be paid (i) in
cash or by check; (ii) in Common Units already owned by the Participant for a
sufficient time (generally six (6) months) to not result in an accounting charge
to the Company, or any combination of cash and Common Units, with the fair
market value of such Common Units valued as of the day prior to delivery; or
(iii) by delivery of a properly executed exercise notice, together with
irrevocable instructions to a broker in a form satisfactory to the Plan
Administrator to promptly deliver to the Company the amount of sale or loan
proceeds to pay the Purchase Price. The Plan Administrator can specify that unit
options granted or to be granted shall permit additional techniques to pay the
Purchase Price. A Participant shall have none of the rights of a unitholder
until the Common Units are issued to the Participant.
 
5.5  TERM OF UNIT OPTIONS
 
     Each unit option shall expire ten (10) years from the date of the granting
thereof, but shall be subject to earlier termination as follows:
 
          (a) In the event that an Participant ceases to be a Director of the
     Company for any reason other than the death of the Participant, the unit
     options granted to such Participant shall expire unless
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     exercised by him or her within thirty-six (36) months after the date such
     Participant ceases to be a Director of the Company.
 
          (b) In the event of the death of a Participant, whether during the
     Participant's service as a Director or during the thirty-six (36) month
     period referred to in Section 5.5(a), the unit options granted to such
     Participant shall be exercisable, and such unit options shall expire unless
     exercised within twelve (12) months after the date of the Participant's
     death, by the legal representatives or the estate of such Participant, by
     any person or persons whom the Participant shall have designated in writing
     on forms prescribed by and filed with the Company or, if no such
     designation has been made, by the person or persons to whom the
     Participant's rights have passed by will or the laws of descent and
     distribution.
 
5.6  TRANSFERABILITY
 
     During an Participant's lifetime, a unit option may be exercised 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 the
applicable laws of descent and distribution except that, to the extent permitted
by applicable law, including Section 16, and Rules promulgated thereunder by the
Securities and Exchange Commission, of the Securities Exchange Act of 1934, as
amended (the "Exchange Act"), 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 unit options in the event of the
Participant's death (as provided in Section 5.5(b)). Any attempt to transfer,
assign, pledge, hypothecate or otherwise dispose of any unit option under the
Plan or of any right or privilege conferred thereby, contrary to the provisions
of the Plan, or the sale or levy or any attachment or similar process upon the
rights and privileges conferred thereby, shall be null and void.
 
5.7  DEFERRAL ELECTION
 
     A Participant may elect irrevocably at any time (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 Units upon exercise of such unit option shall be
deferred until a pre-specified date in the future or until a Participant ceases
to serve as a Director of the Company, 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 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.
 
                                   SECTION 6
 
                               GENERAL PROVISIONS
 
     6.1  Neither the Plan, nor the granting of a unit option, nor any other
action taken pursuant to the Plan shall constitute or be evidence of any
agreement or understanding, express or implied, that a Participant has a right
to continue as a Director for any period of time or at any particular rate of
compensation.
 
     6.2  The Company shall not be required to issue any certificate or
certificates for Units upon the exercise of a unit option granted under the
Plan, or record as a holder of record of Units the name of the individual
exercising a unit option under the Plan, (a) without obtaining to the complete
satisfaction of the Plan Administrator the approval of all regulatory bodies
deemed necessary by the Plan Administrator, and (b) without complying, to the
Plan Administrator's complete satisfaction, with all rules and regulations under
federal, state or local law deemed applicable by the Plan Administrator.
 
     6.3  All costs and expenses of the adoption and administration of the Plan
shall be borne by the Company or the Partnership, as appropriate.
 
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     6.4  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.
 
     6.5  Appropriate provision shall be made for all taxes required to be
withheld in connection with the exercise or other taxable event with respect to
unit options under the applicable laws or regulations of any governmental
authority, whether federal, state or local and whether domestic or foreign.
 
     By participating in the Plan, each Participant shall agree that he or she
is responsible for obtaining qualified tax advice 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.
 
                                   SECTION 7
 
                    EFFECTIVE DATE AND DURATION OF THE PLAN
 
     The Plan shall be effective as of August 14, 1998, subject to the approval
of the plan by the Company's sole stockholder, with such approval to be obtained
within 12 months from the effective date hereof. The Plan shall continue in
effect until it is terminated by action of the Board or the Company's
stockholder, but such termination shall not affect the then-outstanding terms of
any unit options or the Company's obligation to issue Units under any
then-exercised unit options as to which a deferral election has been made under
Section 5.7.
 
                                   SECTION 8
 
                           COMPLIANCE WITH SECTION 16
 
     The Company's intention is that, so long as any of the Partnership'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,
and, if any Plan provision is later found not to be in compliance with such
exemption under Section 16, that provision shall be deemed modified as necessary
to meet the requirements of such applicable exemption.
 
                                   SECTION 9
 
              AMENDMENT, TERMINATION OR DISCONTINUANCE OF THE PLAN
 
     9.1  Subject to the Board and Section 9.2, 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 and the Partnership, including, but not limited to,
any amendment necessary to ensure that the Company and Partnership may obtain
any regulatory approval referred to in Section 6.2; provided, however, that
unless the Plan Administrator determines that such change does not materially
impair the value of the unit options, no change in any unit option theretofore
granted may be made which would impair the right of the Participant to acquire
Units or retain Units that the Participant may have acquired as a result of the
Plan without the consent of the Participant.
 
     9.2  The Board may at any time suspend the operation of or terminate the
Plan with respect to any Units which are not at that time subject to any
outstanding unit options.
 
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     IN WITNESS WHEREOF, the Company has caused the Plan to be executed on
behalf of the Partnership, effective as of August 14, 1998.


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


 
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