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                                                      ITEM 14(a)3, EXHIBIT 10.20


                          TESORO PETROLEUM CORPORATION

                         PHANTOM STOCK OPTION AGREEMENT


         THIS AGREEMENT, effective October 29, 1997, is by and between Bruce A.
Smith, Chairman of the Board of Directors, Chief Executive Officer and
President of Tesoro Petroleum Corporation (the "CEO") and Tesoro Petroleum
Corporation, a Delaware corporation (the "Company").

                                  WITNESSETH:

         WHEREAS, the Compensation Committee of the Board of Directors of the
Company has  determined that a phantom stock option grant should be awarded to
the CEO as stock-related compensation as part of the Company's long term
incentive program and in recognition of the valuable contribution of the CEO
and has directed the Company to enter into this Phantom Stock Option agreement
(the "Agreement") with the CEO;

         NOW, THEREFORE, the Company and the CEO agree as follows:

         1.      GRANT OF OPTION ON PHANTOM STOCK.  The Company hereby grants
to the CEO effective October 29, 1997, ("Date of Grant"), an option on 175,000
notional shares ("Phantom Option Shares") of the Company's common stock, to
receive  cash compensation on the terms and conditions set forth in this
Agreement, with such cash compensation at the time of exercise of the option
being equal to the difference between the average of the highest and lowest
quoted selling prices of the Company's common stock as quoted by the New York
Stock Exchange on the trading date immediately preceding the date of exercise
of the option and $16.9844, which was the average of the highest and lowest
quoted selling prices on the Date of Grant.  This option on Phantom Option
Shares does not create any right of the CEO to shares of the Company's common
stock, but only to receive the cash compensation as provided in this Agreement.
The Company, under the Company's Executive Long-Term Incentive Plan or
successor thereto (hereinafter referred to as the "Plan"), reserves the right
to convert this option to a non-qualified stock option to purchase shares of
the Company's common stock upon approval of the Committee provided for in the
Plan, without the prior consent of the CEO.

         2.      PERIOD OF OPTION.  The option granted herein will expire at
4:00 p.m. Central time on October 28, 2007, (Expiration Time) except that if
the CEO ceases for any reason to be employed by the Company before the
Expiration Time, the option shall terminate, subject to the provisions of
Sections 7,8, 9 and 10 below.

         This option shall not be exercisable unless, at the time of such
exercise, the CEO shall have completed at least twelve (12) months of service
with the Company immediately following the Date of Grant.
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         Leave of absence, if approved in writing by an authorized officer of
the Company, shall not be considered an interruption, cessation or termination
of employment or continuous service for any purpose of this Agreement.

         The right to exercise the option shall occur in four (4) installments.
The first such installment shall vest on the first anniversary of the Date of
Grant and an additional installment shall vest on each succeeding anniversary
of the Date of Grant to and including the fourth such anniversary.  The number
of Phantom Option Shares comprised in each of the first three (3) installments,
shall be equal to fifteen percent (15%) of the total number of Phantom Option
Shares, except that if this creates a number consisting of partial shares, such
installment shall be rounded down to the nearest whole number of shares.  The
number of Phantom Option Shares comprised in the fourth installment shall be
the balance of the Phantom Option Shares.

         The right to exercise this option with respect to the Phantom Option
Shares comprised in each installment is cumulative; i.e., once such right has
become exercisable it may be exercised in whole at any time or in part from
time to time until the termination or expiration of this option.

         3.      EXERCISE AND PAYMENT.  The CEO may exercise this option in
whole or in part (but not as to a fraction of a Phantom Option Share) by giving
written notice to the Company, in a form satisfactory to the Company,
specifying the number of Phantom Option Shares in respect of which the CEO
elects to exercise this option.  This option shall be canceled in relation to
the number of Phantom Option Shares in respect of which this option is
exercised.  Upon each exercise of this option, the Company as promptly as
practicable, shall mail or deliver to the CEO a check in the amount determined
to be due to the CEO in accordance with Section 1 of this Agreement.

         4.      NON-TRANSFERABILITY.  This option and any rights and benefits
under this Agreement may not be sold, transferred, pledged, encumbered,
assigned, or otherwise alienated or hypothecated, other than by will or by the
laws of descent and distribution, and it shall be exercisable, during the
lifetime of the CEO, only by the CEO.

         5.      TERMINATION OF EMPLOYMENT FOR CAUSE.  If the CEO's employment
with the Company is terminated for Cause, all outstanding options under this
Agreement held by the CEO shall be forfeited immediately, and no additional
time for exercise shall be allowed regardless of the vested status of the
options.  For this purpose, "Cause" shall be determined by the Company's Board
of Directors and shall have the meaning set forth in Article 2(f) of the Plan.

         6.      DISABILITY OF RECIPIENT.  If the CEO becomes disabled (within
the meaning of Section 22(e)(3) of the Internal Revenue Code) while the CEO is
employed by the Company  and such employment is terminated by reason of
Disability as defined in Article 2(l) of the Plan, this option shall be
exercisable within, but only within, the period of one year next succeeding the
date that the Company determines the definition of Disability to have been
satisfied, but in no event after the Expiration Time, to the same extent the
CEO was entitled to exercise it on the date of determination of the CEO's
Disability.

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         7.      DEATH OF CEO.  If the CEO dies while employed by the Company
all options which are exercisable as of the date of death shall be exercisable
within, but only within, the period of one year next succeeding the date of
death, but in no event after the Expiration Time, to the same extent the CEO
was entitled to exercise it on the date of the CEO's death.  The term  "CEO,"
as used in this option, shall be deemed to include the estate of the CEO or any
person who acquired the right to exercise this option by bequest or inheritance
or otherwise by reason of the death of the CEO.

         8.      TERMINATION BY RETIREMENT.  In the event that the CEO's
employment is terminated by reason of Retirement as defined in Article 2(ab) of
the Plan, all outstanding options which are exercisable as of the date of
Retirement shall remain exercisable at any time prior to the Expiration Time,
or for three (3) years after the effective date of Retirement, whichever is
shorter.

         9.      EMPLOYMENT TERMINATION FOLLOWED BY DEATH.  In the event that
the CEO's employment terminates by reason of Disability or Retirement, and
within the exercise period following such termination the CEO dies, then the
remaining exercise period under outstanding vested options shall equal the
longer of (i) one (1) year following death; or (ii) the remaining portion of
the exercise period which was triggered by the employment termination.  Such
options shall be exercisable by such person or persons who shall have been
named as the CEO's beneficiary, or by such persons who have acquired the CEO's
rights under the option by will or by the laws of descent and distribution.

         10.     TERMINATION OF EMPLOYMENT FOR OTHER REASONS.  If the CEO's
employment shall terminate for any reason other than Retirement, death,
Disability, for Cause or a Change in Control (as defined in the Plan), all
options held by the CEO which are not vested as of the effective date of such
termination shall be forfeited to the Company.  In the event of termination for
any reason other than Retirement, death, Disability, for Cause or a Change in
Control, options which are vested as of such termination shall remain
exercisable by Recipient for three (3) months after the effective date of such
termination.

         11.     EMPLOYMENT.  This Phantom Stock Option Agreement confers no
right upon the CEO with respect to the continuation of employment with the
Company, and subject to any contractual rights of CEO, shall not interfere with
the right of the Company, or of the CEO, to terminate CEO's employment at any
time.

         12.     ADJUSTMENTS UPON THE OCCURRENCE OF CERTAIN EVENTS.  The
provisions of this Phantom Stock Option Agreement are subject to adjustments in
the event of any merger, reorganization, consolidation, recapitalization,
separation, liquidation, stock dividend, split-up, common stock combination or
other change in the corporate structure of the Company affecting the common
stock of the Company.  The Committee provided for in the Plan, may make such
adjustments as it may determine to be appropriate and equitable, in its sole
discretion, to prevent dilution or enlargement of rights, provided that the
number of Phantom Option Shares subject to this Agreement shall always be a
whole number.





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         13.     CHANGE IN CONTROL.  Upon the occurrence of a Change in Control
of the Company (as defined in the Plan), the provisions of Section  2, above
which require that (i) the CEO shall have completed at least twelve (12) months
of continuous employment with the Company and (ii) the right to exercise this
option shall accrue in four (4) installments, shall be without force or effect,
and any portion of this option which, but for such restrictions, would be
exercisable in full, shall become immediately exercisable in full until this
option shall expire or terminate.

         14.      FUNDING.  It is specifically recognized by the Company and
the CEO that this Agreement is only a general corporate obligation and that the
CEO and the CEO's estate or any person who acquired any right to this Agreement
by bequest or inheritance or otherwise, must rely upon the general credit of
the Company for fulfillment of its obligations under this Agreement.  No
specific assets of the Company have been set aside or pledged in any way for
the performance by the Company of its obligations under this Agreement nor
shall any assets be pledged or set aside in any manner in the future to assure
the performance by the Company of its obligations under this Agreement in any
form in which they cannot be reached by the general creditors of the Company.
It is intended that this Agreement shall be unfunded for tax purposes.

         15.     RESPONSIBILITY FOR WITHHOLDING OF TAXES.  The Company will
calculate the deductions from the amount of the compensation paid under this
Agreement for any taxes required to be withheld by federal, state or local
government and will cause them to be withheld.

         16.     LIMITATION OF RIGHTS.  Nothing in this Agreement will be
construed: (i) to give the CEO any right with respect to any compensation
except under the terms of this Agreement, (ii) to give the CEO or his estate or
any person who acquired any right by bequest or inheritance or otherwise any
interest or right under this Agreement other than that of an unsecured general
creditor of the Company.

         17.     NONALIENATION OF BENEFITS.  No right or benefit provided by
this Agreement is transferable.  No right or benefit under this Agreement will
be subject to anticipation, alienation, sale, assignment, pledge, encumbrance
or charge.  Any attempt to anticipate, alienate, sale, assign, pledge, encumber
or charge the same will be void.  No right or benefit under this Agreement will
be liable for or subject to any debts, contracts, liabilities or torts of the
person entitled to receive the benefit.  Should the CEO or the CEO's estate or
any person who acquired any benefit by bequest or inheritance or otherwise,
become bankrupt or attempt to anticipate, alienate, sell, assign, pledge,
encumber or charge the benefit provided by this Agreement, that benefit will,
in the sole discretion of the Company, cease.  In that event, the Company may
hold or apply the benefit or any part of it for the benefit of the CEO or the
CEO's estate or any person who acquired any benefit by bequest or inheritance
or otherwise, in any manner or in any proportion the Company believes to be
proper in its sole discretion, but it is not required to do so.

         18.     AMENDMENT OR TERMINATION OF THIS AGREEMENT.  This Agreement
may only be modified or terminated by an instrument in writing and executed by
the Company and the CEO.





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         19.     SEVERABILITY.  If any term, provision, covenant or condition
of this Agreement is held to be invalid, void or otherwise unenforceable, the
remaining portions of this Agreement will remain in full force and effect and
will in no way be affected, impaired or invalidated.

         20.     NOTICE.  Any notice hereunder by the CEO shall be given to the
Company in writing and shall be deemed duly given only upon receipt thereof by
the Secretary or an Assistant Secretary of the Company at the Company's office
at 8700 Tesoro Drive, San Antonio, Texas 78217, or at such other address as the
Company may designate by notice to the CEO.  Any notice hereunder by the
Company to the CEO shall be given in writing at such address as the CEO has on
file with the Company.

         21.     INTERPRETATION AND CONSTRUCTION.  The construction and
interpretation of this Phantom Stock Option Agreement is vested in the
Committee provided for in the Plan, and any construction and interpretation by
such Committee shall be final and conclusive, and binding on all parties,
including the Company, the CEO and the CEO's heirs, estate and beneficiary.
The section headings are for convenience of reference only and shall not be
deemed part of, or germane to the interpretation or construction thereof.

         22.     GOVERNING LAW.  This Agreement shall be construed,
administered and governed in all respect by the laws of the State of Texas.

         23.     BINDING EFFECT.  This  Agreement shall be binding upon the
Company, its successors and assigns and the heirs, successors, legal
representatives and other persons claiming by, through or under the CEO.

                                               TESORO PETROLEUM CORPORATION
                                               
                                               By: /s/ JAMES C. REED, JR. 
                                                  ----------------------------
                                                  JAMES C. REED, JR.
                                                  Executive Vice President,
                                                  General Counsel and Secretary



                                               /s/ BRUCE A. SMITH 
                                               -------------------------------
                                               BRUCE A. SMITH





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