EXHIBIT 10.2


                               UNOCAL CORPORATION
                            NONQUALIFIED STOCK OPTION
                   UNDER THE LONG-TERM INCENTIVE PLAN OF 1998


UNOCAL CORPORATION (hereinafter called the "Company"), desiring to provide an
incentive to the success of the Company and its subsidiaries, hereby grants to
Terry G. Dallas (hereinafter called the "Option Holder'), and the Option Holder
hereby accepts, the option to purchase shares of the Common Stock, $1.00 par
value, of the Company (hereinafter "shares") during the Option Period (the
"Option") subject to the Long Term Incentive Plan of 1998, as amended (the
"Plan") and upon the following terms and conditions:

A.       Amount And Term Of Option

1.       This grant is conditioned upon the shareholders of the Company
         approving on or before July 26, 2002 an amendment (whether singly or in
         combination with other changes) to the Plan which amends Section 7
         thereof in a manner consistent with Attachment A. If the shareholders
         of the Company do not approve such an amendment on or prior to July 26,
         2002 this grant shall be null and void and this Option shall terminate.

2.       The exercise price is $36.22 per share, subject to adjustment as
         contemplated by Section 12 of the Plan and paragraphs B.7
         and C.3 below.

3.       The Option Period shall be TEN (10) years, commencing with the date
         this Option is granted. This Option is a Nonqualified Stock Option.
         The date of grant is August 20, 2001.

4.       The total number of shares which may be purchased pursuant to this
         Option shall be 240,000 subject to adjustment as contemplated by
         Section 12 of the Plan and paragraphs B.7 and C.3 below. This Option
         shall become exercisable in accordance with the following schedule:

         50% of the shares may be purchased on or after August 20, 2002 75% of
         the shares may be purchased on or after August 20, 2003 100% of the
         shares may be purchased on or after August 20, 2004

         The Option Holder must be employed by the Company or a subsidiary as of
         each of the above dates for the incremental portion of this Option to
         become exercisable.

B.       Non-Transferability And Lapse Of Option/Termination of Employment

1.       Except as otherwise expressly authorized by the Management Development
         and Compensation Committee of the Board (the "Committee'), this Option
         shall not



         be transferable by the Option Holder except by beneficiary
         designation, will or the laws of descent and distribution and shall be
         exercisable during the Option Holder's lifetime only by the Option
         Holder, or Option Holder's guardian or legal representative, except as
         the Committee may hereafter expressly permit pursuant to Section 11(e)
         of the Plan.

2.       For purposes of this Option, the employment of the Option Holder shall
         be deemed to continue uninterrupted in the event that during the Option
         Period the Option Holder is on authorized sick leave or such other
         leave as is approved by the Committee.

3.       If (a) the employment of the Option Holder by the Company or any of its
         subsidiaries terminates within the Option Period (1) because of
         retirement at or after attaining age 65, (2) because of permanent and
         total disability, or (3) at the convenience of the Company, in its sole
         discretion, and not because of voluntary resignation or performance
         inadequacy, and (b) the Option Holder shall not have then fully
         exercised this Option, then Option Holder shall have the right to
         exercise this Option for not more than the number of shares (subject to
         adjustment as provided in paragraphs C.1 and C.2 of this Option and the
         Plan) which Option Holder was entitled to purchase under this Option on
         the date of such termination of employment. Such exercise right shall
         lapse and this Option shall terminate on the earlier of the third
         anniversary of that date or the end of the Option Period.

4.       If the Option Holder dies during the Option Period without having fully
         exercised this Option, this Option may be exercised within the Option
         Period but not later than fifteen (15) months after the date of the
         death of the Option Holder. If the Option Holder terminates employment
         because of retirement at or after age 65 pursuant to the Company
         retirement plan then in effect or permanent and total disability
         without having fully exercised this Option, the Option may be exercised
         within the Option Period but not after the later of three (3) years
         following such termination, fifteen (15) months after the death of the
         Option Holder or fifteen (15) months after the death of the Option
         Holder's spouse. Exercise of an Option held by a deceased Option Holder
         shall be by the person, persons, trust or trusts duly designated
         by the Option Holder in a form approved by the Company or, in the
         absence of a designation, entitled by will or the laws of descent and
         distribution to receive the benefits specified in this Agreement and
         under the Plan in the event of the Option Holder's death, and shall
         mean the Option Holder's executor or administrator if no other such
         person or entity is designated or authorized to act under the
         circumstances. The Option may not be exercised for more shares than
         the number of shares (subject to adjustment) that Option Holder was
         entitled to purchase on the date of death of the Option Holder.

5.       If the Option Holder's employment with the Company and/or a subsidiary
         terminates other than in the circumstances described in paragraph B.3
         or B.4 above, this Option shall lapse and terminate as of the date of
         such termination of

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         employment.

6.       The Committee may at its sole discretion elect to reinstitute any
         lapsed Options upon the rehire of a terminated Option Holder.

7.       If any Option or other right to acquire Stock hereunder is not
         exercised prior to or in connection with (i) a dissolution of the
         Company, or (ii) a merger, reorganization, consolidation or similar
         event that the Company does not survive, or (iii) a merger,
         reorganization, consolidation or similar event approved by the Board
         (as constituted and acting prior to the event), the Committee may
         provide that the Option or right will terminate, subject to any
         provision that has been expressly made by the Board (as so constituted)
         or by the Committee pursuant to paragraph C.3, through a plan of
         reorganization or otherwise for the survival, assumption, exchange or
         other settlement of the Option or right.

C.       Adjustments To Option Shares

         In addition to adjustments authorized by Section 12 of the Plan:

1.       If the shares then subject to this Option are split, including a split
         in the form of a dividend payable in such shares, then the number of
         shares then subject to this Option (and the number of shares reserved
         for issuance pursuant thereto) shall be increased, and the exercise
         price decreased, proportionately, without any change in the aggregate
         purchase price thereof

2.       If the shares then subject to this Option are the subject of a reverse
         stock split, then the number of shares then subject to this Option (and
         the number of shares reserved for issuance thereafter pursuant thereto)
         shall be decreased, and the exercise price increased, proportionately,
         without any change in the aggregate purchase price thereof.

3.       Subject to paragraph B.7, if the outstanding shares of the Company of
         the class then subject to this Option shall be changed into or
         exchanged for a different number or class of shares of stock of the
         Company or of another entity, whether through reorganization,
         recapitalization, split-up, spin off, combination of shares, merger or
         consolidation, then there shall be, in such manner and to such extent
         (if any) as the Committee deems appropriate in the circumstances,
         substituted for each such share then subject to this Option (and for
         each share reserved for issuance pursuant thereto), the number and
         class of shares of stock or other securities, cash or property (or
         combination thereof) into which each such outstanding share of the
         Company shall be so changed or exchanged, all without any change in the
         aggregate purchase price for the shares then subject to this Option.

                                      -3-




D.       Manner of Exercise

1.       This Option may be exercised from time to time, in accordance with its
         terms, by written notice thereof signed by the Option Holder and
         delivered to the Secretary of the Company at its head office in the
         City of El Segundo, State of California. Such notice shall state the
         number of shares being purchased, be accompanied by payment of the full
         option price for such number of shares and payment for any applicable
         withholding tax (unless otherwise provided for). Payment may be in the
         form of cash or shares of the common stock of the Company (provided the
         shares have been owned at least six (6) months, if originally acquired
         from the Company). Additionally, this Option may be exercised in
         accordance with such other arrangements, including "cashless" exercise
         procedures, as are approved from time to time by the Board or the
         Committee. To the extent exercisable, an Option shall be exercisable
         for all or a part of whole shares, but not as to any fractional
         interest.

2.       The issuance of shares upon the exercise of this Option and subsequent
         transfer thereof shall be subject to all applicable laws, rules and
         regulations with respect to the issuance and sale of such shares, and
         to such approvals by governmental agencies as may be required.

3.       The Option Holder shall be entitled to the privileges of stock
         ownership only as to such shares as are issued or delivered hereunder
         and subject to any limitation under paragraph D.2 above.

4.       Upon the occurrence of a Change in Control Event (as such term is
         defined below), each Option will become immediately exercisable. As
         used herein, "Change in Control Event" means any of the following:

         (a) The acquisition by any individual, entity or group (within the
         meaning of Section 13(d)(3) or 14(d)(2) of the Securities Exchange Act
         of 1934, as amended (the "Exchange Act")(a "Person") of beneficial
         ownership (within the meaning of Rule 13d-3 promulgated under the
         Exchange Act) of 20% or more of either (i) the then outstanding shares
         of common stock of the Company (the "Outstanding Company Common Stock")
         or (ii) the combined voting power of the then outstanding voting
         securities of the Company entitled to vote generally in the election of
         directors (the "outstanding Company Voting Securities"); provided,
         however, that for purposes of this subsection (a), the following
         acquisitions shall not constitute a Change of Control: (i) any
         acquisition directly from the Company, (ii) any acquisition by the
         Company, (iii) any acquisition by an employee benefit plan (or related
         trust) sponsored or maintained by the Company or any corporation
         controlled by the Company or (iv) any acquisition by any corporation
         pursuant to a transaction which complies with clauses (i), (ii) and
         (iii) of subsection (c) of this Section D.4;

         (b) Individuals who, as of the date hereof, constitute the Board (the
         "Incumbent

                                      -4-


         Board") cease for any reason to constitute at least a
         majority of the Board; provided, however, that any individual becoming
         a director subsequent to the date hereof whose election, or nomination
         for election by the Company's shareholders, was approved by a vote of
         at least a majority of the directors then comprising the Incumbent
         Board shall be considered as though such individual were a member of
         the Incumbent Board, but excluding, for this purpose, any such
         individual whose initial assumption of office occurs as a result of an
         actual or threatened election contest with respect to the election or
         removal of directors or other actual or threatened solicitation of
         proxies or consents by or on behalf of a Person other than the Board;
         or

         (c) Consummation of a reorganization, merger or consolidation or sale
         or other disposition of all or substantially all of the assets of the
         Company or the acquisition of assets of another corporation (a
         "Business Combination"), in each case, unless, following such Business
         Combination, (i) all or substantially all of the individuals and
         entities who were the beneficial owners, respectively, of the
         Outstanding Company Common Stock and Outstanding Company Voting
         Securities immediately prior to such Business Combination will
         beneficially own, directly or indirectly, more than 50% of
         respectively, the then outstanding shares of common stock and the
         combined voting power of the outstanding voting securities entitled to
         vote generally in the election of directors, as the case may be, of the
         corporation resulting from such Business Combination (including,
         without limitation, a corporation which as a result of such transaction
         owns the Company or all or substantially all of the Company's assets
         either directly or through one or more subsidiaries) in substantially
         the same proportions as their ownership, immediately prior to such
         Business Combination of the Outstanding Company Common Stock and
         Outstanding Company Voting Securities, as the case may be, (ii) no
         Person (excluding any corporation resulting from such Business
         Combination or any employee benefit plan (or related trust) of the
         Company or such corporation resulting from such Business Combination)
         will beneficially own, directly or indirectly, 20% or more of
         respectively, the then outstanding shares of common stock of the
         corporation resulting from such Business Combination or the combined
         voting power of the then outstanding voting securities of such
         corporation except to the extent that such ownership existed prior to
         the Business Combination and (iii) at least a majority of the members
         of the board of directors of the corporation resulting from such
         Business Combination were members of the Incumbent Board at the time of
         the execution of the initial agreement, or of the action of the Board,
         providing for such Business Combination; or

         (d)      Approval by the shareholders of the Company of a complete
         liquidation or dissolution of the Company.

E.       Miscellaneous

1.       This Option is granted pursuant to the Plan and is subject to all of
         the terms and

                                      -5-


         provisions of the Plan.

2.       As further consideration for the granting of this Option, the Option
         Holder agrees to continue in the employment of the Company or one or
         more of its subsidiaries at the pleasure of the Company or such
         subsidiary for a continuous period of at least one (1) year from date
         hereof at the salary rate in effect on the date hereof or at such
         changed rate as may be fixed from time to time by the Company or such
         subsidiary. Except as permitted by Section 7(d)(iv) of the Plan, the
         Option Holder agrees during such employment to devote Option Holder's
         entire time, energy and skills to the service and interests of
         the Company or such subsidiary, to promote its interest, and to act in
         accord with the regular policies of the Company and its subsidiaries.

3.       This Option shall not confer upon the Option Holder any right with
         respect to continuance of employment by the Company or any subsidiary,
         nor shall it interfere in any way with Option Holder's status as an "at
         will" employee or with the right of the Company or any subsidiary to
         terminate employment at any time for any reason, with or without cause.

4.       Notwithstanding any other provision hereof, in the event of a public
         tender for all or any portion of the stock of the Company or in the
         event that a proposal to merge, consolidate, or otherwise combine with
         another company is submitted for shareholder approval, the Committee
         may in its sole discretion declare previously granted options to be
         immediately exercisable.

5.       The headings of this Agreement are solely for convenience and shall not
         be given any effect in interpreting this Agreement.

6.       This Agreement has been executed in two counterparts each of which
         shall constitute one and the same instrument.

         IN WITNESS WHEREOF, The Company has granted this Option, at El Segundo,
California effective on August 20, 2001, which date is the date of grant of this
Option.

                                           UNOCAL CORPORATION


                                           By:  /s/CHARLES R. WILLIAMSON
                                                ------------------------
                                                  Charles R. Williamson
                                                 Chief Executive Officer

ACCEPTED:  /s/TERRY G. DALLAS
           --------------------

PRINT NAME:  Terry G. Dallas
             ------------------------------------

DATE:     29 August 01
       ------------------------------------------

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                                                                   Attachment A


            Amendment to Long Term Incentive Plan of 1998, as amended

                        (subject to shareholder approval)

Effective upon shareholder approval on or before July 25, 2002 of an amendment
or amendments to the Plan including the following change, the second sentence of
Section 7 of the Plan shall be revised to read as follows:

          "No person may be granted during any 12-month period Options
           to acquire more than 600,000 shares of Stock under this Plan.






                   NOTATIONS AS TO PARTIAL EXERCISE OF OPTION


- ------------------------- ------------------------- ------------------------
                                  Number of                 Balance of
        Date of                     Shares                   Shares on
       Exercise                   Exercised                   Option

- ------------------------- ------------------------- ------------------------