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                                                                 EXHIBIT 10.2(b)


                    2001 CONDITIONAL STOCK UNIT AWARD PROGRAM
                                    UNDER THE
              1998 INCENTIVE PLAN OF PENNZOIL-QUAKER STATE COMPANY


                  1. Program. This 2001 Conditional Stock Unit Award Program
(this "Program") was adopted by the Committee under the 1998 Incentive Plan of
Pennzoil-Quaker State Company, as amended from time to time (the "Plan"), as a
vehicle for the grant of certain Stock Awards thereunder. The Committee retains
the right to amend, modify or terminate this Program at any time, provided that
no Common Stock Unit previously awarded hereunder shall be adversely affected.

                  2. Definitions. Capitalized terms used herein shall have the
meanings ascribed to them in the Plan or, if not defined in the Plan, the
meanings set forth below:

                  "Award Cycle" means a five-year period with respect to which
Units are awarded.

                  "Award Year" means the first Plan Year of each Award Cycle,
during which Units are granted to Program Participants.

                  "Common Stock Unit" means a unit awarded a Program Participant
hereunder for the purpose of measuring the benefits payable hereunder that shall
be deemed a Stock Award for all purposes of the Plan.

                  "Fiscal Year" means the year commencing January 1 and ending
December 31.

                  "Matured Units" means Units which are distributable in the
form of Common Stock.

                  "Payment Year" means the Plan Year following the close of the
five-year term of each Award Cycle, during which distribution of shares of
Common Stock equal to the number of Matured Units for such Award Cycle is to be
made.

                  "Plan Year" means a Fiscal Year.

                  "Program Participant" means an Employee who is awarded Common
Stock Units under this Program.

                  "Unit" means a Common Stock Unit.

                  3. Operation. This Program shall consist of one or more Award
Cycles, one of which shall commence on January 1, 2001. The Committee, in its
discretion, may establish an additional Award Cycle as of any January 1
thereafter during the continuance of this Program.

                  4. Designation of Program Participants. During the Award Year
of each Award Cycle, the Committee shall designate and notify in writing the
Program Participants in that Award Cycle and shall advise each such Program
Participant of the number of Units awarded to him under such Award Cycle.



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                  5. Common Stock Units and Dividend Equivalents.

                  (a) Establishment of Common Stock Unit Ledger. The Company
shall set up an appropriate record (the "Common Stock Unit Ledger") that shall
from time to time reflect the name of each Program Participant and the number of
Units awarded to him under each Award Cycle.

                  (b) Dividend Equivalents. On each dividend payment date with
respect to Common Stock, the Company shall pay to each Program Participant who
is in the employ of the Company or any Subsidiary, or who has terminated such
employment under circumstances that avoid the forfeiture of his Units as
provided in Section 6(a) hereof, a cash payment equal to the number of Units
credited to the account of the Program Participant in the Common Stock Unit
Ledger as of the appropriate dividend record date times the dollar amount of the
dividend paid on such dividend payment date on each share of Common Stock. It is
intended that the amount of the payment shall be equivalent to the dividend that
such Program Participant would have received had he been the owner of a number
of shares of Common Stock equal to the number of Units credited to him on the
dividend record date. Notwithstanding the foregoing, no amount shall be paid
with respect to Units held by a Program Participant on a dividend record date
but forfeited by him prior to the dividend payment date.

                  6. Distributions.

                  (a) Conversion of Units Into Matured Units. Units awarded
under each Award Cycle shall become Matured Units at the close of the five-year
term of the Award Cycle as provided below. Units awarded any Program Participant
under the Award Cycle that were not previously forfeited shall become Matured
Units only if:

                           (i) the Program Participant was employed by the
         Company or any Subsidiary at the end of the five-year term of the Award
         Cycle;

                           (ii) the Program Participant has terminated
         employment during the term of the Award Cycle because of death,
         disability (as determined in the discretion of the Committee), or
         retirement after attaining age 65 (or at an earlier age if specifically
         approved for this purpose in writing by the Committee) and completing
         at least five (5) years of employment with the Company and its
         Subsidiaries; or

                           (iii) the Committee determines for any reason and
         subject to such conditions as it may determine appropriate to permit
         the Units to become Matured Units.

If a Program Participant shall terminate his employment with the Company or any
Subsidiary during the term of an Award Cycle, then all Units awarded such
Program Participant that have not become Matured Units shall be forfeited unless
such Units are to become Matured Units pursuant to the preceding sentence.
Notwithstanding the foregoing, upon the dissolution or liquidation of the
Company, all Units which have not previously been forfeited shall become Matured
Units.

                  (b) Distribution of Common Stock. A number of shares of Common
Stock equal to the number of Matured Units held by each Program Participant
shall be distributed to



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each such Program Participant as soon as practicable after the close of the
five-year term of the Award Cycle, except as provided in subsection (d) of this
Section 6.

                  (c) Beneficiary Designations. Each person becoming a Program
Participant shall file with the Company a designation of one or more
beneficiaries to whom distributions otherwise due the Program Participant shall
be made in the event of his death while in the employ of the Company or any
Subsidiary or after termination of employment but prior to the distribution of
Common Stock attributable to any Matured Units (or cash out) as specified in
Section 6(b) or Section 6(d). The Program Participant shall have the right to
change the beneficiary or beneficiaries from time to time; provided, however,
that any change shall not become effective until received in writing by the
Company. If there is no effective beneficiary designation on file at the time of
a Program Participant's death, or if the designated beneficiary or beneficiaries
have all predeceased such Program Participant, the payment of any remaining
benefits shall be made to the Program Participant's estate. If the beneficiary
or beneficiaries shall survive the Program Participant but shall die before
receiving all of the benefits hereunder, any remaining benefits shall be
distributed to the deceased distributee's estate.

                  (d) Acceleration of Benefits.

                           (i) Upon Change in Control. Notwithstanding any
         provision of this Program to the contrary, in the event of the
         occurrence of a Change in Control (as defined herein), each Program
         Participant under an Award Cycle shall receive a cash payment equal to
         the product of (A) the number of Units awarded to the Program
         Participant under each Award Cycle of this Program as of the effective
         date of such Change in Control and (B) the value (as defined herein)
         per share of the Common Stock. Such payment shall be in lieu of any
         benefits otherwise payable under this Program in respect of such Units.
         As used herein, a "Change in Control" shall conclusively be deemed to
         have occurred (x) if the Board determines by resolution that a Change
         in Control that has a reasonable likelihood of depriving Employees of
         benefits they otherwise would have earned, by depriving Employees of
         the opportunity to fulfill applicable service and age prerequisites to
         benefits or otherwise has occurred, or (y) upon the occurrence of an
         event specified for such purposes as a "change in control" that has the
         reasonable likelihood of depriving employees of benefits they otherwise
         would have earned by depriving Employees of the opportunity to fulfill
         applicable service and age prerequisites to benefits or otherwise, by
         resolution of the Board adopted not later than sixty (60) days prior to
         the occurrence of such event. The effective date of a Change in Control
         shall be (1), in the case of such a Change in Control determined as
         specified in clause (x) of the preceding sentence, the date (not more
         than thirty days prior to the date on which the Board makes the
         determination) the Board determines as of the date on which the Change
         in Control has occurred or (2) in the case of such a Change in Control
         determined as specified in clause (y) of the preceding sentence, the
         date of occurrence of the event specified by the Board as constituting
         such Change in Control. "Value" as used herein of a share of Common
         Stock shall mean the amount determined to be the fair value per share
         thereof by the Board in the resolution or resolutions adopted by it
         determining that a Change in Control has occurred or will occur upon
         the occurrence of events specified as a Change in Control, or, in the
         absence of any determination of fair value by the Board, the average of
         the closing prices per share of the Common Stock on the New York Stock
         Exchange



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         Composite Tape during the ten (10) trading days immediately prior to
         the effective date. In the event the Board determines the fair value,
         the amount so determined shall be not less than the ten-day average
         price computed in accordance with the preceding sentence and not in
         excess of an amount (assuming that such amount is in excess of such
         ten-day average) equal to the highest consideration paid for the Common
         Stock and any offer to the holders thereof made as a part or in
         connection with the transaction or transactions resulting in the Change
         in Control.

                           (ii) Upon Increase in Share Value. Notwithstanding
         any provision of the Program to the contrary, with respect to the Award
         Cycle commencing on January 1, 2001:

                                    (a) In the event that the average Fair
                  Market Value of a share of Common Stock for any twenty (20)
                  consecutive business day period ("20-Day Period") equals or
                  exceeds $22.03, as determined by the Committee (the "First
                  Threshold"), prior to an event described in Section 6(a),
                  6(d)(i), or 6(d)(ii)(b), then forty percent (40%) of the Units
                  (rounded up to the next whole number) awarded to the Program
                  Participant for such Award Cycle shall become Matured Units as
                  of the date of the First Threshold. A number of shares of
                  Common Stock equal to the number of such Matured Units shall
                  be distributed to such Program Participant as soon as
                  practicable after the date of the First Threshold, and the
                  total number of Units awarded to the Program Participant for
                  such Award Cycle shall be reduced by the number of such
                  Matured Units.

                                    (b) In the event that the average Fair
                  Market Value of a share of Common Stock of the Company for any
                  20-Day Period equals or exceeds $31.72, as determined by the
                  Committee (the "Second Threshold"), prior to an event
                  described in Section 6(a), 6(d)(i), or 6(d)(ii)(a), then one
                  hundred percent (100%) of the Units (if applicable, as
                  adjusted by Section 6(d)(ii)(a)) awarded to the Program
                  Participant for such Award Cycle shall become Matured Units as
                  of the date of the Second Threshold. A number of shares of
                  Common Stock equal to the number of such Matured Units (not
                  previously distributed under Section 6(d)(ii)(a)) shall be
                  distributed to such Program Participant as soon as practicable
                  after the date of the Second Threshold.

         A distribution of shares of Common Stock under this Section 6(d)(ii)
         shall be in lieu of any benefits otherwise payable under this Program
         in respect of such Matured Units.

                  7. Rights of Program Participants.

                  (a) Limitation of Rights. Nothing in this Program shall be
construed to:

                           (i) Give any Employee of the Company or a Subsidiary
                           any right to be awarded any Units other than in the
                           sole discretion of the Committee;

                           (ii) Give a Program Participant any rights whatsoever
                           with respect to shares of Common Stock prior to the
                           date Units held by the Participant become Matured
                           Units, except as provided in Section 6(d) hereof;



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                           (iii) Limit in any way the right of the Company or
                           any Subsidiary to terminate a Program Participant's
                           employment with the Company or any Subsidiary at any
                           time;

                           (iv) Give a Program Participant or any other person
                           any interest in any fund or in any specific asset or
                           assets of the Company or any Subsidiary; or

                           (v) Be evidence of any agreement or understanding,
                           express or implied, that the Company or any
                           Subsidiary will employ a Program Participant in any
                           particular position or at any particular rate of
                           remuneration.

                  (b) Nonalienation of Benefits. No right or benefit under this
         Program shall be subject to anticipation, alienation, sale, assignment,
         pledge, encumbrance or charge, and any attempt to anticipate, alienate,
         sell, assign, pledge, encumber or charge the same will be void. No
         right or benefit hereunder shall in any manner be liable for or subject
         to any debts, contracts, liabilities or torts of the person entitled to
         such benefits. If any Program Participant or beneficiary hereunder
         shall become bankrupt or attempt to anticipate, alienate, sell, assign,
         pledge, encumber or charge any right or benefit hereunder, or if any
         creditor shall attempt to subject the same to a writ of garnishment,
         attachment, execution, sequestration or any other form of process or
         involuntary lien or seizure, then such right or benefit shall, in the
         discretion of the Committee, either cease and terminate absolutely or
         be held by the Company for the sole benefit of the Program Participant
         or the beneficiary, his spouse, children or other dependents, or any of
         them in such manner and in such proportion as the Committee shall deem
         proper, free and clear of the claims of any other party whatsoever.

                  (c) Prerequisites to Benefits. No Program Participant, or any
         person claiming through a Program Participant, shall have any right or
         interest in this Program or the Award Cycles, or any benefits
         hereunder, unless and until all the terms, conditions and provisions of
         the Award Cycle that affect such Program Participant or such other
         person shall have been complied with as specified herein.


                                              PENNZOIL-QUAKER STATE COMPANY


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