TESORO PETROLEUM CORPORATION

                 BOARD OF DIRECTORS DEFERRED PHANTOM STOCK PLAN




                          TESORO PETROLEUM CORPORATION
                 BOARD OF DIRECTORS DEFERRED PHANTOM STOCK PLAN

                               TABLE OF CONTENTS

                                                                  Section

ARTICLE I -- DEFINITIONS

    Account. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1
    Beneficiary. . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2
    Board of Directors . . . . . . . . . . . . . . . . . . . . . . . .1.3
    Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.4
    Committee. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.5
    Common Stock . . . . . . . . . . . . . . . . . . . . . . . . . . .1.6
    Deferred Phantom Stock Ledger. . . . . . . . . . . . . . . . . . .1.7
    Disability . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.8
    Effective Date . . . . . . . . . . . . . . . . . . . . . . . . . .1.9
    NYSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10
    Participant. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11
    Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.12
    Plan Year. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.13
    Retirement . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.14
    Tesoro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.15

ARTICLE II - ELIGIBILITY

ARTICLE III - INITIAL TRANSFER, YEARLY ACCRUAL AND DEFERRALS

    Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1
    Yearly Accrual . . . . . . . . . . . . . . . . . . . . . . . . . .3.2
    Election to Defer. . . . . . . . . . . . . . . . . . . . . . . . .3.3
    Failure to Elect . . . . . . . . . . . . . . . . . . . . . . . . .3.4
    Revocation of Election . . . . . . . . . . . . . . . . . . . . . .3.5
    Timing and Form of Election. . . . . . . . . . . . . . . . . . . .3.6

ARTICLE IV - ACCOUNT

    Establishing a Participant's Account . . . . . . . . . . . . . . .4.1
    Credit of Initial Transfer, Yearly Accruals and Deferrals. . . . .4.2
    Crediting of Dividends and Distributions . . . . . . . . . . . . .4.3

ARTICLE V - VESTING

    Deferrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1

                                      -i-

                         TABLE OF CONTENTS (CONTINUED)

                                                                  Section

    Yearly Accrual . . . . . . . . . . . . . . . . . . . . . . . . . .5.2
    Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3
    General Vesting Provisions . . . . . . . . . . . . . . . . . . . .5.4

ARTICLE VI - DISTRIBUTIONS

    Form and Period of Distribution. . . . . . . . . . . . . . . . . .6.1
    Death/Beneficiary Designation. . . . . . . . . . . . . . . . . . .6.2
    Disability . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3
    Retirement . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.4
    Cessation as a Director Prior to Death, Disability or Retirement .6.5
    Responsibility for Distributions and
      Withholding of Taxes . . . . . . . . . . . . . . . . . . . . . .6.6

ARTICLE VII - ADMINISTRATION

    Committee Appointment. . . . . . . . . . . . . . . . . . . . . . .7.1
    Committee Organization and Voting. . . . . . . . . . . . . . . . .7.2
    Powers of the Committee. . . . . . . . . . . . . . . . . . . . . .7.3
    Committee Discretion . . . . . . . . . . . . . . . . . . . . . . .7.4
    Annual Statements. . . . . . . . . . . . . . . . . . . . . . . . .7.5
    Reimbursement of Expenses. . . . . . . . . . . . . . . . . . . . .7.6

ARTICLE VIII - AMENDMENT AND/OR TERMINATION

    Amendment or Termination of the Plan . . . . . . . . . . . . . . .8.1
    No Retroactive Effect on Account . . . . . . . . . . . . . . . . .8.2
    Effect of Termination. . . . . . . . . . . . . . . . . . . . . . .8.3

ARTICLE IX - FUNDING


ARTICLE X - MISCELLANEOUS

    Limitation of Rights . . . . . . . . . . . . . . . . . . . . . . 10.1
    Distributions to Incompetents or Minors. . . . . . . . . . . . . 10.2
    Nonalienation of Benefits. . . . . . . . . . . . . . . . . . . . 10.3
    Reliance Upon Information  . . . . . . . . . . . . . . . . . . . 10.4
    Severability . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5

                                      -ii-

                         TABLE OF CONTENTS (CONTINUED)

                                                                  Section

    Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6
    Gender and Number. . . . . . . . . . . . . . . . . . . . . . . . 10.7
    Governing Law. . . . . . . . . . . . . . . . . . . . . . . . . . 10.8

                                     -iii-


                          TESORO PETROLEUM CORPORATION

                 BOARD OF DIRECTORS DEFERRED PHANTOM STOCK PLAN


         WHEREAS, Tesoro Petroleum  Corporation  has  previously  established  a
Non-Employee  Director  Retirement  Plan  (the  "Director  Retirement Plan") for
non-employee members of the Board of Directors;

         WHEREAS, the Board of  Directors  wishes to align Director compensation
more directly with the shareholders' interest;

         WHEREAS, the Board of Directors has determined that it is more  in  the
interest  of the shareholders to amend the Director Retirement Plan so as to (i)
freeze that plan and convert all of  the interest of the current Directors under
the plan to a lump sum present value which will be transferred to and become the
initial Account balance of the Directors in  the  Tesoro  Petroleum  Corporation
Board  of  Directors  Deferred  Phantom  Stock  Plan and (ii) provide for future
annual accruals to the  Account  balance  of  the  Directors,  so that after the
amendment and transfer only those retired Directors  who  have  begun  receiving
benefits  under the Director's Retirement Plan shall remain participants in that
plan;

         WHEREAS, the Board  of  Directors  has  determined  that  it  is in the
interest of shareholders to allow Directors to defer all or part of the  portion
of  their  annual  retainer  not  paid  in  restricted  stock into their Account
hereunder;

         WHEREAS, the  Board  of  Directors  has  now  determined  the terms and
conditions of the Tesoro  Petroleum  Corporation  Board  of  Directors  Deferred
Phantom Stock Plan and wish to formally establish the plan;


         NOW,  THEREFORE,  Tesoro  Petroleum Corporation through this instrument
establishes the Tesoro Petroleum Corporation Board of Directors Deferred Phantom
Stock Plan which shall be as follows:

                                   ARTICLE I

                                  DEFINITIONS


         1.1    ACCOUNT.   "Account"  means  a   Participant's  Account  in  the
Deferred Phantom Stock Ledger maintained by the  Committee  which  reflects  the
benefits a Participant is entitled to under this Plan.

         1.2    BENEFICIARY.   "Beneficiary" means a person or entity designated
by the  Participant  under  the  terms  of  this  Plan  to  receive  any amounts
distributed under the Plan upon the death of the Participant.

         1.3    BOARD OF DIRECTORS.  "Board of Directors"  means  the  Board  of
Directors of Tesoro.

         1.4    CODE.   "Code"  means  the  Internal  Revenue  Code  of 1986, as
amended from time to time.

         1.5    COMMITTEE.  "Committee" means the  persons  who are from time to
time serving as the Tesoro Petroleum Corporation Retirement Plan Committee.

         1.6 COMMON STOCK.  "Common Stock"  means  the $.16-2/3 par value common
stock of Tesoro.

         1.7    DEFERRED  PHANTOM STOCK LEDGER.  "Deferred Phantom Stock Ledger"
means the  ledger  maintained  by  the  Committee  for  all  Participants, which
reflects the amount transferred from the Director Retirement  Plan,  the  yearly
accrual to each Participant under this


Plan,  the  one time committee chairman accrual to a Participant under this Plan
and the amount of each Participant's  director  retainer fees for the year which
is eligible for deferral if it has been deferred  by  the  Participant  and  the
amount of dividends credited to his Account.

         1.8    DISABILITY.   "Disability"  means a physical or mental condition
that meets the eligibility  requirements  for  the  receipt of disability income
under the federal Social Security Act.

         1.9    EFFECTIVE DATE.  "Effective Date" means March 6, 1997.

         1.10   NYSE.  "NYSE" shall mean the New York Stock Exchange, or, if the
Common Stock is no longer traded on such exchange, the principal stock  exchange
or other securities market in which the Common Stock is publicly traded.

         1.11   PARTICIPANT.   "Participant"  means  a  member  of  the Board of
Directors of Tesoro who is not  otherwise  employed by Tesoro or a subsidiary of
Tesoro.

         1.12   PLAN.  "Plan" means the Tesoro Petroleum  Corporation  Board  of
Directors  Deferred  Phantom  Stock  Plan set forth in this document, as amended
from time to time.

         1.13   PLAN YEAR.  "Plan Year" means the calendar year.

         1.14   RETIREMENT.  "Retirement" or "Retires" means the retirement of a
Participant from the Board of Directors  of  Tesoro  as a result of reaching the
age when he no longer may stand for  election  under  the  Company's  Governance
Policy  or  otherwise  ceasing  to be a Director after service of at least three
years as a director and  the  Board  by  a  duly adopted resolution declares the
Participant to have retired.

         1.15   TESORO.  "Tesoro" means the Tesoro Petroleum Corporation.

                                      I-2

                                   ARTICLE II

                                  ELIGIBILITY


         All members of the Board of Directors who are  not  otherwise  employed
and have not been employed within the last three years by Tesoro or a subsidiary
of  Tesoro will be eligible to participate in this Plan.  Any eligible member of
the Board of Directors will automatically  become a Participant in this Plan.

                                      II-1

                                  ARTICLE III

                 INITIAL TRANSFER, YEARLY ACCRUAL AND DEFERRALS


         3.1    TRANSFER.   Upon the establishment of the Plan the present value
of the lump sum accrued benefit  of  each  Director  listed in Exhibit A to this
Plan shall be transferred from the Director Retirement Plan to this  Plan.   The
transfer  shall  be credited to his Account in the Deferred Phantom Stock Ledger
as of the Effective  Date  of  this  Plan.   By  participating in, and accepting
benefits under, this Plan, as acknowledged in writing, each Director waives  any
and all rights he may have under the Director Retirement Plan.

         3.2    YEARLY  ACCRUAL.   Each  Plan  Year,  commencing with 1997, each
Participant shall have credited  to  his  Account  in the Deferred Phantom Stock
Ledger as of the last day of the Plan  Year  the  sum  of  $7,250.00;  and  each
Participant  who  is  serving  as  a  chairman  of  a  committee of the Board of
Directors immediately prior to his termination  as a director and who has served
at least three years as a director shall have an additional amount of  $5,000.00
credited  to  his account in the Deferred Phantom Stock Ledger as of the date he
ceases to be a director.  The yearly accruals for being a member of the Board of
Directors are  limited  to  15  full  annual  accruals  (partial  accruals being
aggregated for the purposes of this limitation), taking into  account  both  the
previous  accruals  of  retirement  benefits  under the Director Retirement Plan
(based on the Effective Date  of  service  as  listed in Exhibit A) and accruals
under this Plan.  In the event a director only serves for part of a  Plan  year,
the $7,250 accrued shall be pro rated based on the actual number of days served.

         3.3    ELECTION TO DEFER.  Each Participant shall  have  the  right  to
elect  to  defer  any  part  or  all  of the cash portion of his annual director
retainer fee.  The election to defer is

                                     III-1

effective  only  if  received  by  the  Committee  in  proper  form prior to the
beginning of the Plan Year or Years  for  which  it is to be applicable.  Once a
Plan Year has commenced the election to defer becomes irrevocable for that  Plan
Year  and  shall  remain  in  effect for all subsequent Plan Years until revoked
pursuant to Section  3.5.   The  initial  election  to  defer  will be effective
immediately for any director retainer fees not yet paid.

         3.4    FAILURE  TO  ELECT.   If  the  Committee  fails  to  receive   a
Participant's  election in proper form prior to the beginning of a Plan Year for
which no prior election is  effective,  the  Participant  will be deemed to have
elected not to defer the cash portion of his director  retainer  fees  for  that
Plan Year.

         3.5    REVOCATION  OF  ELECTION.  Each Participant shall have the right
to revoke any prior election to defer  the cash portion of his director retainer
fees.  Any revocation of election shall be effective only on a prospective basis
beginning with the Plan Year next  following  the  Committee's  receipt  of  the
revocation  in  proper  form.  If the Committee fails to receive a Participant's
election for revocation of election in  proper  form prior to the beginning of a
Plan Year, the Participant will be deemed to have  elected  to  defer  the  cash
portion  of  his  director  retainer  fees in the same percentage as his current
deferral.

         3.6    TIMING AND FORM OF ELECTION.  The Committee shall have the right
to make such  rules  and  regulations  regarding  the  election or revocation of
election to defer as are not inconsistent with the requirements of Sections 3.3,
3.4 and 3.5, including establishing election periods, forms for election and all
other pertinent matters.

                                     III-2

                                   ARTICLE IV

                                    ACCOUNT


         4.1    ESTABLISHING  A  PARTICIPANT'S  ACCOUNT.   The  Committee   will
establish  an  Account  for each Participant in a special Deferred Phantom Stock
Ledger which will be maintained by  Tesoro.  The Account will reflect the amount
of Tesoro's obligation to the Participant.

         4.2    CREDIT  OF  INITIAL TRANSFER, YEARLY ACCRUALS AND DEFERRALS.  As
of the Effective Date of  this  Plan  the  Committee shall have credited to each
Participant's Account in the Deferred Phantom  Stock  Plan  Ledger  the  present
value  of  the  accrued benefit of that Participant set out in Exhibit A to this
Plan, which has been transferred from the Director Retirement Plan to this Plan.
Then, upon completion of each Plan  Year  on  the  last day of the Plan Year the
Committee will credit to each Participant $7,250.00 and to each Participant  who
is serving as a chairman of a committee of the Board of Directors at the time of
his  termination  as  a  director  and  who has served at least three years as a
director, an additional $5,000.00  on  the  date  of  termination as a director.
Finally, upon completion of each quarter of  the  fiscal  year  of  Tesoro,  the
Committee will determine, as soon as administratively practicable, the amount of
each  Participant's  director  retainer  fees  that  have been deferred for that
quarter and will credit that amount to the Participant's Account in the Deferred
Phantom Stock Ledger as of the  last  business day of that fiscal quarter.  Each
transfer, accrual or deferral shall be credited to the Participant's Account  in
units  based  upon  the number of shares, including fractions thereof, of Common
Stock that could have been  purchased  with  the dollar amount credited, without
taking

                                      IV-1


into account any brokerage fees, taxes or other expenses which might be incurred
in such a transaction, based upon the closing quotation on the NYSE on the  date
the amount is credited.

         4.3    CREDITING OF DIVIDENDS AND DISTRIBUTIONS.   When  dividends  are
declared and paid, or other distributions, whether stock, property, cash, rights
or  other  are  made  with  respect  to  the  Common  Stock,  those dividends or
distributions shall be accrued in  a  Participant's Account based upon the units
then  credited  to  the  Participant's  Account.    The   dividends   or   other
distributions  in  the  form  of shares of Common Stock shall be credited to the
Account as additional units.  The dividends  or other distributions or rights in
any other form, other than Common Stock, shall be valued at fair market value as
determined, in the case of non cash distributions, by resolutions  duly  adopted
by the Committee and shall then be credited to each Account as additional units.
The  procedure for determining the number of units shall be that used in Section
4.2, including any fractional shares.   All  such  units shall be credited as of
the date the dividend or distribution upon which the unit is based  is  paid  or
issued.

                                      IV-2

                                   ARTICLE V

                                    VESTING


         5.1    DEFERRALS.   All  director  retainer  fees  which  are  deferred
pursuant  to  Section  3.3 under an election by the Director and are credited to
his Account in the Deferred Phantom  Stock  Ledger  as well as the $5000 accrual
for acting as a chairman of a committee of the Board of  Directors  pursuant  to
Section  3.2  shall  be  100%  vested at all times, together with their pro rata
share of all appreciation or depreciation and all income earned.

         5.2    YEARLY ACCRUAL.  All  yearly  accruals  pursuant  to Section 3.2
credited to a Director's Account in the Deferred Phantom Stock Ledger,  together
with  their  pro  rata  share of all appreciation or depreciation and all income
earned, shall immediately vest in full  once the Participant has completed three
full years of service (including all service prior to the Effective Date)  as  a
member of the Board of Directors.

         5.3    TRANSFER.   The  present value of the accrued benefit previously
awarded a member of the  Board  of  Directors under the Director Retirement Plan
listed in Exhibit A that has been transferred to this Plan  and  credited  to  a
Director's Account in the Deferred Phantom Stock Ledger shall be 100% vested for
all  Directors  who  have  served  three  full years as a member of the Board of
Directors prior to the date hereof and all other Directors shall vest 100% after
the Director has served three full years  as  a member of the Board of Directors
(including service prior to the date hereof), together with its pro  rata  share
of all appreciation or depreciation and all income earned.

         5.4    GENERAL  VESTING PROVISIONS.  Service for the purpose of vesting
under this Article V shall  commence  on  the  date of the Participant's initial
election to the Board of

                                      V-1

Directors.  If a Director voluntarily resigns or is removed from  the  Board  of
Directors,  or  is  not re-elected to the Board, prior to meeting the three full
years of service requirement, he shall  forfeit all amounts not then vested.  If
a Director dies, Retires or becomes disabled, he shall be  100%  vested  in  all
amounts  credited  to  his Account without regard to his years of service on the
Board of Directors.

                                      V-2

                                   ARTICLE VI

                                 DISTRIBUTIONS


         6.1    FORM AND PERIOD OF DISTRIBUTION.

              (a)    Election, Revocation or Change of  Election of the Form and
    Period of Distribution.  Each Participant shall have the right to elect,  to
    revoke,  or  to  change  any  prior  election  of  the  form  and  period of
    distribution at the time and  under  the rules established by the Committee;
    provided that the initial election hereunder must be made within 60 days  of
    the  Effective  Date  or within 30 days of a Participant's first election to
    the Board  of  Directors.   The  initial  election  of  form  and  period of
    distribution if received by the Committee in proper form shall be  effective
    immediately.  All other elections of form and period of distribution and all
    revocations  or changes of election of form and period of distribution shall
    be effective only if the election,  revocation  or change is received by the
    Committee in proper form one year  prior  to  the  event  which  requires  a
    distribution  under  this  Plan.   During  that one year period prior to the
    effective date of  an  election,  revocation  or  change, the last effective
    election, revocation or change made by the  Participant  shall  continue  to
    remain in force.

              (b)    Option  As  to  Period  of Distribution.  A Participant may
    elect either a total distribution, which  distribution shall be made 30 days
    after the event requiring  distribution,  or  annual  installments,  not  to
    exceed ten years, the first installment of which shall be made 30 days after
    the  event  occurs  which  requires  distribution and each succeeding annual
    installment being made on the same  day of each succeeding calendar year, or
    if such day is not a normal business day, the next business day,  until  the
    entire

                                      VI-1

    Account  has  been  fully distributed.  If the Participant elects to receive
    annual installments, then the entire Account shall be divided in to a number
    of equal parts equal  to  the  number  of  the installments.  Each such part
    shall continue to appreciate or depreciate  and  to  accrue  income  thereon
    until such time as a part is to be distributed as an installment.

              (c)    No  Effective  Election.  If there is no effective election
    as to form or period  of  distribution the Participant shall be conclusively
    deemed to have elected one total distribution.

              (d)    Type of Distribution.  Each distribution shall be in  cash.
    The Common Stock in the Account with respect to which the distribution is to
    be made shall be valued at the closing quotation on the NYSE on the business
    day immediately preceding the date on which the cash distribution is made.

              (e)    Event    Requiring   Distributions.    Death,   disability,
    Retirement or cessation as a  Director  as contemplated by Section 6.5 shall
    constitute an event requiring a distribution.

         6.2    DEATH/BENEFICIARY DESIGNATION.  Upon the death of a Participant,
the Participant's Beneficiary or Beneficiaries will receive the  cash  value  of
the  balance as of the date of death then credited plus any pro rata amounts not
yet posted to the Participant's Account in the Deferred Phantom Stock Ledger.

         Each Participant, at the time  of making his initial deferral election,
must file with the Committee a designation of one or more Beneficiaries to  whom
distributions  otherwise  due  the  Participant will be made in the event of his
death prior to the  complete  distribution  of  the Participant's Account in the
Deferred Phantom Stock Ledger.  The designation will be effective

                                      VI-2

upon receipt by the Committee of a properly executed form  which  the  Committee
has  approved for that purpose.  The Participant may from time to time revoke or
change any designation  of  Beneficiary  by  filing another approved Beneficiary
designation form with the Committee.   If  there  is  no  valid  designation  of
Beneficiary  on  file with the Committee at the time of the Participant's death,
or if all of the  Beneficiaries  designated  in the last Beneficiary designation
have predeceased the Participant or otherwise ceased to exist,  the  Beneficiary
will  be  the  Participant's  spouse, if the spouse survives the Participant, or
otherwise the Participant's estate.  A  Beneficiary must survive the Participant
by 60 days in  order  to  be  considered  to  be  living  on  the  date  of  the
Participant's  death.   If  any Beneficiary survives the Participant but dies or
otherwise ceases to exist before receiving  all amounts due the Beneficiary from
the Participant's Account, the balance of the amount which would have been  paid
to   that  Beneficiary  will,  unless  the  Participant's  designation  provides
otherwise, be distributed to the  individual deceased Beneficiary's estate or to
the Participant's  estate  in  the  case  of  a  Beneficiary  which  is  not  an
individual.   Any  Beneficiary designation which designates any person or entity
other than the Participant's spouse must  include the written consent, in a form
acceptable to the Committee, of the spouse in order to be effective.

         6.3    DISABILITY.  Upon incurring a Disability, the Participant  shall
receive  his entire Account in the Deferred Phantom Stock Ledger at the time and
in the manner provided in Section 6.1.

         6.4    RETIREMENT.  Upon Retirement, the  Participant shall receive his
entire Account in the Deferred Phantom Stock Ledger  at  the  time  and  in  the
manner provided in Section 6.1.

                                      VI-3

         6.5    CESSATION   AS   A   DIRECTOR  PRIOR  TO  DEATH,  DISABILITY  OR
RETIREMENT.  Upon a Participant's  ceasing  to  serve  on the Board of Directors
after three full years of service on the Board of Directors,  other  than  as  a
result  of  death,  Disability  or Retirement, the Participant shall receive his
entire Account in the Deferred Compensation  Ledger which has vested at the time
and in the manner provided in Section 6.1.

         6.6    RESPONSIBILITY FOR DISTRIBUTIONS AND WITHHOLDING OF TAXES.   The
Committee  will  furnish information to Tesoro concerning the period and form of
distribution to be made to  any  Participant  entitled to a distribution so that
Tesoro can make the distribution required.  The Committee  will  also  calculate
the  deductions  to  be made from all distributions under the Plan for any taxes
required to be withheld by  federal,  state  or  local government and will cause
them to be withheld.

                                      VI-4

                                  ARTICLE VII

                                 ADMINISTRATION


         7.1    COMMITTEE APPOINTMENT.  The Committee will be comprised  of  the
Tesoro Petroleum Corporation Retirement Committee as it is constituted from time
to time.  The Board of Directors will have the sole discretion to remove any one
or  more  Committee  members  and  appoint one or more replacement or additional
Committee members from time to time.

         7.2    COMMITTEE ORGANIZATION AND  VOTING.   The  Committee will select
from among its members a chairman who will preside at all of  its  meetings  and
will  elect a secretary without regard to whether that person is a member of the
Committee.  The secretary will keep  all  records, documents and data pertaining
to the Committee's supervision and administration of the Plan.   A  majority  of
the  members  of  the  Committee will constitute a quorum for the transaction of
business and the vote of a majority  of  the members present at any meeting will
decide any question brought before the meeting.  In addition, the Committee  may
decide  any  question  by  vote,  taken  without a meeting, of a majority of its
members.  A member of the Committee who  is  also a Participant will not vote or
act on any matter relating solely to himself.

         7.3    POWERS OF THE COMMITTEE.  The Committee will have the  exclusive
responsibility for the general administration of the Plan according to the terms
and  provisions  of  the  Plan  and will have all powers necessary to accomplish
those purposes, including but  not  by  way  of  limitation the right, power and
authority:

              (a)    to make rules and regulations for the administration of the
    Plan;

              (b)    to  construe  all   terms,   provisions,   conditions   and
    limitations of the Plan;

                                     VII-1

              (c)    to correct any defect, supply any omission or reconcile any
    inconsistency that may appear in the Plan in the manner and to the extent it
    deems  expedient  to  carry the Plan into effect for the greatest benefit of
    all parties at interest;

              (d)    to designate the persons eligible to become Participants;

              (e)    to   determine   all    controversies   relating   to   the
    administration of the Plan, including but not limited to:

                   (i)   differences of opinion arising  between  Tesoro  and  a
    Participant; and

                   (ii)   any  question it deems advisable to determine in order
    to promote the uniform administration  of  the  Plan  for the benefit of all
    parties at interest; and

              (f)    to  delegate  by  written   notice   those   clerical   and
    recordation  duties of the Committee, as it deems necessary or advisable for
    the proper and efficient administration of the Plan.

         7.4    COMMITTEE DISCRETION.  The Committee  in exercising any power or
authority granted under this Plan or in making any determination under this Plan
shall perform or refrain from performing those acts using  its  sole  discretion
and  judgment.   Any  decision made by the Committee or any refraining to act or
any act taken by the Committee in  good  faith shall be final and binding on all
parties.  The Committee's decision shall be final and binding on all parties and
shall not be subject to review.

         7.5    ANNUAL STATEMENTS.  The Committee will cause each Participant to
receive an annual statement as soon as administratively  practicable  after  the
conclusion of each Plan Year containing the units credited to his Account during
that Plan Year, the total units credited

                                     VII-2

to  his  Account at the end of the Plan Year and the value of those units at the
end of the Plan Year.

         7.6    REIMBURSEMENT OF  EXPENSES.   The  Committee  will serve without
compensation for their services  but  will  be  reimbursed  by  Tesoro  for  all
expenses properly and actually incurred in the performance of their duties under
the Plan.

                                     VII-3

                                  ARTICLE VIII

                          AMENDMENT AND/OR TERMINATION


         8.1    AMENDMENT  OR TERMINATION OF THE PLAN.  The members of the Board
of Directors may amend or terminate  this  Plan  at any time by an instrument in
writing.

         8.2    NO RETROACTIVE EFFECT ON ACCOUNT.  No amendment will affect  the
rights  of  any  Participant  to  the  units  then standing to his credit in his
Account in the Deferred Phantom Stock Ledger or change the method of valuing the
units then credited to his Account without the Participant's consent.

         8.3    EFFECT  OF  TERMINATION.   If   the  Plan  is  terminated,  each
Participant's Account shall become fully vested.  Distribution shall commence in
accordance with Section 6.4 as  if  the  Participant  Retired  on  the  date  of
termination of the Plan as soon as conveniently practicable.

                                     VIII-1

                                   ARTICLE IX

                                    FUNDING


         It  is specifically recognized by both Tesoro and the Participants that
this Plan is only a general  corporate commitment and that each Participant must
rely upon the general credit of Tesoro for the fulfillment of  its  obligations.
Under  all  circumstances the rights of Participants to any asset held by Tesoro
will be  no  greater  than  the  rights  expressed  in  this agreement.  Nothing
contained in this agreement will constitute  a  guarantee  by  Tesoro  that  the
assets of Tesoro will be sufficient to pay any benefits under this Plan or would
place  the  Participant  in  a  secured  position  ahead of general creditors of
Tesoro.  The Plan will not create  any lien, claim, encumbrance, right, title or
other interest of any kind whatsoever in any Participant in any  asset  held  by
Tesoro.  No specific assets of Tesoro have been or will be set aside, or will in
any  way  be  transferred  to  any  trust  or will be pledged in any way for the
performance of Tesoro's obligations  under  this  Plan  which would remove those
assets from being subject to the general creditors of Tesoro.

                                      IX-1

                                   ARTICLE X

                                 MISCELLANEOUS


         10.1   LIMITATION OF RIGHTS.  Nothing in this Plan will be construed:

              (a)    to give a Participant any right with respect to any  amount
    credited in the Deferred Phantom Stock Ledger, except in accordance with the
    terms of this Plan;

              (b)    to  limit  in  any  way  the  right  of  Tesoro to remove a
    Participant from the Board of Directors at any time;

              (c)    to evidence any  agreement  or  understanding, expressed or
    implied, that Tesoro will retain a Participant as a member of the  Board  of
    Directors for any particular remuneration; or

              (d)    to  give a Participant or any other person claiming through
    him any interest or right under  this  Plan other than that of any unsecured
    general creditor of Tesoro.

         10.2   DISTRIBUTIONS TO INCOMPETENTS OR MINORS.  Should  a  Participant
become  incompetent  or  should  a  Participant designate a Beneficiary who is a
minor or incompetent, the Committee is authorized to distribute any funds due to
the parent of the  minor  or  to  the  guardian  of  the minor or incompetent or
directly to the minor or to apply those funds for the benefit of  the  minor  or
incompetent in any manner the Committee determines in its sole discretion.

         10.3   NONALIENATION OF BENEFITS.  No right or benefit provided in this
Plan  will be transferable by the Participant except, upon his death, to a named
Beneficiary as provided in this Plan.  No  right or benefit under this Plan will
be subject to anticipation, alienation, sale, assignment, pledge, encumbrance or
charge, and any attempt to anticipate, alienate, sell, assign,

                                      X-1

pledge, encumber, or charge the same will be void.  No right  or  benefit  under
this  Plan  will in any manner be liable for or subject to any debts, contracts,
liabilities or torts of the person entitled to a benefit.  If any Participant or
any Beneficiary becomes  bankrupt  or  attempts  to  anticipate, alienate, sell,
assign, pledge, encumber or charge any right or benefit under  this  Plan,  that
right  or  benefit  will,  in  the  discretion of the Committee, cease.  In that
event, the Committee may have Tesoro hold  or  apply the right or benefit or any
part of it to the benefit of the Participant or Beneficiary, his or her  spouse,
children  or other dependents or any of them in any manner and in any proportion
the Committee believes to be proper in  its sole and absolute discretion, but is
not required to do so.

         10.4   RELIANCE UPON INFORMATION.  The Committee will not be liable for
any decision or action taken in good faith in connection with the administration
of this Plan.  Without limiting the generality of the foregoing, any decision or
action taken by the Committee when it relies upon information supplied it by any
officer of Tesoro, Tesoro's legal counsel, Tesoro's independent  accountants  or
other advisors in connection with the administration of this Plan will be deemed
to have been taken in good faith.

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

         10.6   NOTICE.  Any notice or filing required or permitted to be  given
to  the  Committee  or  a  Participant will be sufficient if in writing and hand
delivered or sent by U.S.  mail  to  the  principal  office  of Tesoro or to the
residential mailing address of the Participant.  Notice will  be  deemed  to  be
given  as of the date of hand delivery or if delivery is by mail, as of the date
shown on the postmark.

                                      X-2

         10.7   GENDER AND NUMBER.  Words used in this Plan of one gender are to
be construed as though they were also  used in another gender in all cases where
they would so apply and likewise words in the  singular  or  plural  are  to  be
construed  as  though they also included the other in all cases where they would
so apply.

         10.8   GOVERNING LAW.  The  Plan  will  be  construed, administered and
governed in all respects by the laws of the State of Texas.

         IN WITNESS WHEREOF, Tesoro has executed this document on this 24th  day
of  April 1997, as authorized by the Board of Directors of Tesoro on the 6th day
of March 1997.

                             TESORO PETROLEUM CORPORATION



                             By /S/ James C. Reed, Jr.
                                    James C. Reed, Jr.
                                    Executive Vice President,
                                    General Counsel and Secretary

                                      X-3

                                   EXHIBIT A


         Present Value of Accrued Retirement  Benefit under the Tesoro Petroleum
Corporation Directors' Retirement Plan which was transferred to this Plan on the
Effective Date.



                            Present Value
                             of Accrued
                         Benefit as of March 1,     Effective Date of
      Director                  1997                    Service

Caverly, Robert J.                   147,440           04/30/92

Grapstein, Steven H.                  29,557           04/30/92

Johnson, William J.                    9,056           06/06/96

Kaufman, Alan J.                       9,462           04/12/96

Mason, Raymond K.                    149,922           04/27/83

Ward, Patrick J.                      14,194           03/11/96

Weidenbaum, Murray L.                 74,924           04/30/92

                                      X-4