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                                                                   EXHIBIT 10.32

                           UNOCAL EMPLOYMENT AGREEMENT

       This employment agreement (the "Agreement") is made effective as of March
12, 2003 by and between Unocal Corporation, a Delaware corporation (the
"Company") and Terry G. Dallas ("Employee").

       In consideration of the mutual promises and agreements set forth herein,
the Company and Employee agree as follows:

1.     TERM.

       1.1    The term of this Agreement (the "Term") shall commence on March
12, 2003 and shall be for three (3) years, subject to earlier termination in
accordance with the provisions of Section 4 hereinbelow. If the Agreement has
not been subject to early termination in accordance with the provisions of
Section 4 hereinbelow, beginning on March 12, 2003 and on each day thereafter,
the Term shall automatically be extended for an additional day unless the
Company notifies Employee in writing that it does not wish to further extend the
Term. Notwithstanding the foregoing, this Agreement shall end automatically and
without additional notice on the date of the Company's Annual Meeting of
Shareholders that next follows the date of Employee's sixty-fifth (65th)
birthday.

2.     POSITION AND TITLE.

       2.1    The Company on behalf of itself and its affiliates and
subsidiaries hereby employs Employee as Executive Vice President & Chief
Financial Officer and Employee hereby accepts such employment.

       2.2    Employee shall devote substantially all of his efforts on a full
time basis to the business and affairs of the Company and shall not engage in
any business or perform any services in any capacity whatsoever adverse to the
interests of the Company.

       2.3    Employee shall at all times faithfully, industriously, and to the
best of his ability, experience, and talents, perform all of the duties of his
position.

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3.     COMPENSATION.

       3.1    As of the date of this Agreement, Employee's annual base salary is
$449,400. Employee's base salary and performance shall be reviewed periodically
at intervals approved by the Management Development and Compensation Committee
of the Board of Directors of the Company (the "Committee"), and Employee's base
salary may be increased from time to time based on merit or such other
consideration as the Committee may deem appropriate.

       3.2    During the Term, Employee shall participate in all of the
Company's incentive plans, benefit plans and perquisites, and in any new or
successor incentive plans, benefit plans and perquisites, that are generally
provided to executives of the Company with a level of responsibility and stature
comparable to Employee. Performance goals, award opportunity, benefit levels,
and administrative guidelines for such plans shall be subject to review and
approval by the Committee.

4.     TERMINATION OF EMPLOYMENT.

       4.1    During the Term, the Company may terminate Employee's employment
herein at any time for Cause or as a result of a material breach by Employee of
his obligations under this Agreement, provided however that, except in the case
of conviction of a felony, the Company shall provide Employee with not less than
sixty (60) days prior written notice describing the behavior or conduct which is
alleged by the Company to constitute Cause, and Employee shall be provided with
reasonable opportunity to correct such behavior or conduct within the notice
period. For purposes of this Agreement, Cause shall be defined as any or all of
the following:

       (1)  Conduct or action by Employee which, in the opinion of a majority of
            the Board of Directors, is materially harmful to the Company;

       (2)  Willful failure by Employee to follow an order of the Board, except
            in such case where the Employee believes in good faith that
            following such order would be materially detrimental to the
            interests of the Company;

       (3)  Employee's conviction of a felony.

       4.2    In the event that Employee's employment is terminated by the
Company for any reason other than those set forth in Paragraph 4.1 hereinabove,
or, (a) Employee's annual base salary is reduced below the amount stated in
Paragraph 3.1 hereinabove (unless such reduction is part of an across the board
reduction affecting all Company executives with a comparable level of
responsibility, title or stature), or (b) Employee is removed from or denied

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participation in incentive plans, benefit plans, or perquisites generally
provided by the Company to other executives with a comparable level of
responsibility, title or stature, or (c) Employee's target incentive
opportunity, benefits or perquisites are reduced relative to other executives
with comparable responsibility, title or stature, or (d) Employee is assigned
duties or obligations inconsistent with his position with the Company or (e)
There is a significant change in the nature and scope of Employee's authority or
his overall working environment, or (f) Employee's work location following a
Change In Control would result in an increase in his or her one way commute by
at least 50 miles from the existing residence, such event shall be considered a
Termination Without Cause.

       4.3    In the event of Employee's Termination Without Cause at any time
during the Term of this Agreement, then:

       (1)  The Company shall pay Employee a lump-sum severance amount within
            thirty (30) days following Termination Without Cause equal to three
            (3) times the sum of (a) the higher of the Employee's annual base
            salary at the time of Termination Without Cause or the annual base
            salary stated in Paragraph 3.1 hereinabove, and (b) the annual
            target Bonus applicable to Employee as of the beginning of the
            calendar year in which such Termination Without Cause occurs. Such
            sum shall be reduced by the amount of any Unocal Employee
            Redeployment Program and Unocal Termination Allowance benefits
            payable to Employee; and further reduced by any Change of Control
            enhancements (determined by the increase in the lump sum amounts
            payable to Employee) under the Unocal Retirement Plan and the
            non-qualified retirement plans of the Company.

       (2)  The Company shall provide for Employee to receive medical, dental,
            life, and disability insurance coverage for two (2) years following
            Termination Without Cause at levels and a net cost to Employee
            comparable to that provided to Employee immediately prior to
            Employee's Termination Without Cause. In lieu of the foregoing
            continued benefits, the Company in its sole discretion may elect to
            pay the Employee the sum of $25,000 (twenty-five thousand U.S.
            Dollars).

       (3)  The Company shall pay Employee an additional lump-sum severance
            amount within thirty (30) days following Employee's Termination
            Without Cause equal to three (3) times the base salary used to
            determine the lump-sum severance benefit in paragraph 4.3(1)
            hereinabove, multiplied by 6% (.06).

       4.4    In the event that during the Term of this Agreement Employee
should voluntarily resign from the Company, should terminate employment with the
Company due to death, permanent disability or incapacitation, or is

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terminated by the Company for Cause or for a material breach by Employee of his
obligations under this Agreement, then Employee shall not be entitled to any of
the termination benefits provided for in Paragraph 4.3 hereinabove, and the Term
of the Agreement shall immediately end.

       4.5    Employee shall not be obligated to seek other employment or take
any other action by way of mitigation of the amounts payable to Employee under
any provisions of this Agreement.

5.     CHANGE OF CONTROL.

       5.1    In the event of a Change of Control of the Company at any time
during the Term of this Agreement, then:

       (1)  In the event of Employee's Termination Without Cause within a period
            of twenty-four (24) months following the date of a Change of
            Control, Employee shall be entitled to the termination benefits
            described in Paragraph 4.3 hereinabove plus the benefit described in
            Section 5.1(2) below.

       (2)  The Employee shall be entitled to an amount equal to the increase in
            the lump sum value of Employee's Unocal Retirement Plan and
            non-qualified retirement plans of the Company if three years were
            added to Employee's benefit service and age thereunder. Such amount
            shall be payable hereunder notwithstanding Section 4.3(1) above.

       5.2    For the purpose of this Agreement, a "Change of Control" shall
mean:

       (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 5.2; or

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       (b)    Individuals who, as of the date hereof, constitute the Board (the
"Incumbent 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 beneficially
own, directly or indirectly, more than 50% of, respectively, the then
outstanding shares of common stock and the combined voting power of the then
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) beneficially owns, 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.

       5.3    Certain Additional Payments by the Company may be due as follows:

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       (a)    Anything in this Agreement to the contrary notwithstanding and
except as set forth below, in the event it shall be determined that any payment
or distribution by the Company or its affiliates to or for the benefit of the
Employee (whether paid or payable or distributed or distributable pursuant to
the terms of this Agreement or otherwise but determined without regard to any
additional payments required under this Section 5.3), (a "Payment") would be
subject to the excise tax imposed by Section 4999 of the Code or any interest or
penalties are incurred by the Employee with respect to such excise tax (such
excise tax, together with any such interest and penalties, are hereinafter
collectively referred to as the "Excise Tax"), then the Employee shall be
entitled to receive an additional payment (a "Gross-Up Payment") in an amount
such that after payment by the Employee of all taxes (including any interest or
penalties imposed with respect to such taxes), including, without limitation,
any income taxes (and any interest and penalties imposed with respect thereto)
and Excise Tax imposed upon the Gross-Up Payment, the Employee retains an amount
of the Gross-Up Payment equal to the Excise Tax imposed upon the Payments.
Notwithstanding the foregoing provisions of this Section 5.3, if it shall be
determined that the Employee is entitled to a Gross-Up Payment, but that the
Payments do not exceed 110% of the greatest amount (the "Reduced Amount") that
could be paid to the Employee such that the receipt of Payments would not give
rise to any Excise Tax, then no Gross-Up Payment shall be made to the Employee
and the Payments, in the aggregate, shall be reduced to the Reduced Amount.

       (b)    Subject to the provisions of Section 5.3(c), all determinations
required to be made under this Section 5.3, including whether and when a
Gross-Up Payment is required and the amount of such Gross-Up Payment and the
assumptions to be utilized in arriving at such determination, shall be made by
Ernst and Young or such other certified public accounting firm as may be
designated by the Employee (the "Accounting Firm") which shall provide detailed
supporting calculations both to the Company and the Employee within 15 business
days of the receipt of notice from the Employee that there has been a Payment,
or such earlier time as is requested by the Company. In the event that the
Accounting Firm is serving as accountant or auditor for the individual, entity
or group effecting the Change of Control, the Employee shall appoint another
nationally recognized accounting firm to make the determinations required
hereunder (which accounting firm shall then be referred to as the Accounting
Firm hereunder). All fees and expenses of the Accounting Firm shall be borne
solely by the Company. Any Gross-Up Payment, as determined pursuant to this
Section 5.3, shall be paid by the Company to the Employee within five days of
the receipt of the Accounting Firm's determination. Any determination by the
Accounting Firm shall be binding upon the Company and the Employee. As a result
of the uncertainty in the application of Section 4999 of the Code at the time of
the initial determination by the Accounting Firm hereunder, it is possible that
Gross-Up Payments which will not have been made by the Company should

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have been made ("Underpayment"), consistent with the calculations required to be
made hereunder. In the event that the Company exhausts its remedies pursuant to
Section 5.3(c) and the Employee thereafter is required to make a payment of any
Excise Tax, the Accounting Firm shall determine the amount of the Underpayment
that has occurred and any such Underpayment shall be promptly paid by the
Company to or for the benefit of the Employee.

       (c)    The Employee shall notify the Company in writing of any claim by
the Internal Revenue Service that, if successful, would require the payment by
the Company of the Gross-Up Payment. Such notification shall be given as soon as
practicable but no later than ten business days after the Employee is informed
in writing of such claim and shall apprise the Company of the nature of such
claim and the date on which such claim is requested to be paid. The Employee
shall not pay such claim prior to the expiration of the 30-day period following
the date on which it gives such notice to the Company (or such shorter period
ending on the date that any payment of taxes with respect to such claim is due).
If the Company notifies the Employee in writing prior to the expiration of such
period that it desires to contest such claim, the Employee shall:

       (i)    give the Company any information reasonably requested by the
              Company relating to such claim,

       (ii)   take such action in connection with contesting such claim as the
              Company shall reasonably request in writing from time to time,
              including, without limitation, accepting legal representation with
              respect to such claim by an attorney reasonably selected by the
              Company,

       (iii)  cooperate with the Company in good faith in order effectively to
              contest such claim, and

       (iv)   permit the Company to participate in any proceedings relating to
              such claim; provided, however, that the Company shall bear and pay
              directly all costs and expenses (including additional interest and
              penalties) incurred in connection with such contest and shall
              indemnify and hold the Employee harmless, on an after-tax basis,
              for any Excise Tax or income tax (including interest and penalties
              with respect thereto) imposed as a result of such representation
              and payment of costs and expenses. Without limitation on the
              foregoing provisions of this Section 5.3(c), the Company shall
              control all proceedings taken in connection with such contest and,
              at its sole option, may pursue or forgo any and all administrative
              appeals, proceedings, hearings and conferences with the taxing
              authority in respect of such claim and may, at its sole option,
              either direct the Employee to pay the tax claimed and sue for a
              refund or contest the claim in any permissible manner, and the
              Employee agrees to prosecute such contest to a determination
              before any administrative

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              tribunal, in a court of initial jurisdiction and in one or more
              appellate courts, as the Company shall determine; provided,
              however, that if the Company directs the Employee to pay such
              claim and sue for a refund, the Company shall advance the amount
              of such payment to the Employee, on an interest-free basis and
              shall indemnify and hold the Employee harmless, on an after-tax
              basis, from any Excise Tax or income tax (including interest or
              penalties with respect thereto) imposed with respect to the such
              advance or with respect to any imputed income with respect to such
              advance; and further provided that any extension of the statute of
              limitations relating to payment of taxes for the taxable year of
              the Employee with respect to which such contested amount is
              claimed to be due is limited solely to such contested amount.
              Furthermore, the Company's control of the contest shall be limited
              to issues with respect to which a Gross-Up Payment would be
              payable hereunder and the Employee shall be entitled to settle or
              contest, as the case may be, any other issue raised by the
              Internal Revenue Service or any other taxing authority.

       (d)    If, after the receipt by the Employee of an amount advanced by the
              Company pursuant to Section 5.3(c), the Employee becomes entitled
              to receive any refund with respect to such claim, the Employee
              shall (subject to the Company's employing with the requirements of
              Section 5.3 promptly pay to the Company the amount of such refund
              (together with any interest paid or credited thereon after taxes
              applicable thereto). If, after the receipt by the Employee of an
              amount advanced by the Company pursuant to Section 5.3(c), a
              determination is made that the Employee shall not be entitled to
              any refund with respect to such claim and the Company does not
              notify the Employee in writing of its intent to contest such
              denial of refund prior to the expiration of 30 days after such
              determination, then such advance shall be forgiven and shall not
              be required to be repaid and the amount of such advance shall
              offset, to the extent thereof, the amount of Gross-Up Payment
              required to be paid.

6.     COVENANTS.

       6.1    Employee agrees that any and all confidential knowledge or
information, including but not limited to customer lists, books, records, data,
formulae, specifications, inventions, processes and methods, and developments
and improvements, which have been or may be obtained or learned by Employee in
the course of his employment with the Company, will be held confidential by
Employee, and that Employee shall not disclose the same to any person outside of
the Company either during his employment with the Company or after his
employment by the Company has terminated.

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       6.2    Employee agrees that upon termination of his employment with the
Company he will immediately surrender and turn over to the Company all books,
records, forms, specifications, formulae, data, and all papers and writings
relating to the business of the Company and all other property belonging to the
Company, it being understood and agreed that the same are the sole property of
the Company and that Employee shall not make or retain any copies thereof.

       6.3    Employee agrees that all inventions, developments or improvements
which he has made or may make, conceive, invent, discover or otherwise acquire
during his employment with the Company in the scope of his responsibilities or
otherwise shall become the sole property of the Company.

       6.4    Employee agrees to provide a release of any claims with respect to
termination of his or her employment on such form as requested by the Company
upon payment of the sums provided in Section 4.3 above.

7.     MISCELLANEOUS PROVISIONS.

       7.1    All terms and conditions of this Agreement are set forth herein,
and there are no warranties, agreements or understandings, express or implied,
except those expressly set forth herein.

       7.2    Any modification to this Agreement shall be binding only if
evidenced in writing signed by all parties hereto. This Agreement replaces and
supercedes that Unocal Employment Agreement between Company and Employee dated
May 30, 2000 in its entirety.

       7.3    Any notice or other communication required or permitted to be
given hereunder shall be deemed properly given if personally delivered or
deposited in the United States mail, registered or certified and postage
prepaid, addressed to the Company at 2141 Rosecrans Ave., Suite 4000, El
Segundo, CA (Attention: General Counsel), or to Employee at his or her most
recent home address on file with Company, or at other such addresses as may from
time to time be designated in writing by the respective parties.

       7.4    The laws of the State of California shall govern the validity of
this Agreement, the construction of its terms, and the interpretation of the
rights and duties of the parties involved.

       7.5    In the event that any one or more of the provisions contained in
this Agreement shall for any reason be held to be invalid, illegal or
unenforceable, the same shall not affect any other provision of this Agreement,
but this Agreement shall be construed as if such invalid, illegal or
unenforceable provisions had never been contained herein.

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       7.6    This Agreement shall be binding upon, and inure to the benefit of,
the successors and assigns of the Company and the personal representatives,
heirs and legatees of Employee.

       7.7    "Bonus" refers to the Unocal Incentive Compensation Plan and any
replacement or successor plan thereof.

       7.8    Company shall pay 90% (ninety percent) of Employee's out-of-pocket
litigation expenses, including reasonable attorney's fees, in connection with
any judicial proceeding to enforce this Agreement or construe or determine the
validity of this Agreement, whether or not the Employee is successful in such
proceeding.

       7.9    The term "Company" shall include with respect to employment
hereunder, any subsidiary or affiliate of the Company, as well as any successor
employer following a Change in Control.

IN WITNESS WHEREOF, the parties have executed this Agreement effective as of the
date first above written.


BY:      /s/ Charles R. Williamson
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         Charles R. Williamson for the Management Development
         and Compensation Committee of the Unocal
         Board of Directors


BY:      /s/ Terry G. Dallas
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