<PAGE>   1

                                                                    EXHIBIT 10.6

                          PENNZOIL-QUAKER STATE COMPANY

                          SUPPLEMENTAL DISABILITY PLAN

I. PURPOSE OF PLAN, DEFINITIONS AND DURATION.

         1.1 Purposes. This Supplemental Disability Plan (the "Plan") of
Pennzoil-Quaker State Company (the "Company") for selected executives is
intended to attract and retain executives of outstanding competence and ability
by providing financial security to them in the event of their disability during
employment.

         1.2 Definitions.

                  (a) "Company" means Pennzoil-Quaker State Company or any
         successor.

                  (b) "Subsidiary" means any corporation in which the Company
         owns, directly or indirectly, stock possessing 50% or more of the total
         combined voting power of all classes of stock or any affiliated company
         which is controlled by the Company by reason of a management contract
         and stock ownership.

                  (c) "Board" means the Board of Directors of the Company.

                  (d) "Closing Date" means the date of Closing as described in
         the Agreement and Plan of Merger, dated as of April 14, 1998, among
         Pennzoil Company, Pennzoil Products Company, Downstream Merger Company
         and Quaker State Corporation ("Merger Agreement").

                  (e) "Employee" means any person, including an officer of the
         Company or any Subsidiary (whether or not he is also a director
         thereof), who, at the time such person is designated a Participant
         hereunder, is employed by the Company or any Subsidiary on a full-time
         basis, who is compensated for such employment by a regular salary and
         who, in the opinion of the Committee, is one of the officers or other
         key executives of the Company or any Subsidiary in a position to
         contribute materially to the continued growth and development and to
         the future financial success of the Company.

                  (f) "Participant" means an Employee who has been designated by
         the Committee to participate in the Plan. The term Participant also
         means any individual who (1) immediately prior to the "Distribution
         Date," was receiving a benefit under the PennzEnergy Company
         Supplemental Disability Plan (formerly, the Pennzoil Company
         Supplemental Disability Plan), and (2) is either (i) a "Downstream
         Employee" not actively at work, (ii) a "Downstream Former Employee," as
         terms in quotes are defined in the Merger Agreement,



                                      -1-
<PAGE>   2


         or (iii) a former employee of Pennzoil Company who is assigned to the
         Company under the Merger Agreement.

                  (g) "Retirement Plan" means the Pennzoil-Quaker State Company
         Salaried Employees Retirement Plan.

                  (h) "Normal Retirement Date" means the normal retirement date
         under the Retirement Plan.

         1.3 Term. The effective date of the Plan is the Closing Date. The Plan
shall continue until terminated by the Board as herein provided.


II. ADMINISTRATION OF THE PLAN - COMMITTEE.

         2.1 Appointment of Committee. The Plan shall be administered by the
Compensation Committee or such other committee of the Board as may be designated
by the Board from time to time ("the Committee").

         2.2 Committee Powers. The Committee shall be deemed to have and to be
exercising all of the powers of the Board in the performance of any of the
powers and duties delegated to it under the Plan, including, but without
limiting the generality of the foregoing, the selection of Participants. The
Committee may from time to time establish rules for the administration of the
Plan which are not inconsistent with the provision and purposes of the Plan.

         2.3 Committee Action. A majority of the members of the Committee shall
constitute a quorum for the transaction of business. All action taken by the
Committee at a meeting shall be by the vote of a majority of those present at
such meeting, but any action may be taken by the Committee without a meeting
upon written consent signed by all of the members of the Committee. Members of
the Committee may participate in a meeting by means of conference telephone or
similar communications equipment by means of which all persons participating in
the meeting can hear each other.

         2.4 Committee Determinations Conclusive. The determination of the
Committee as to any disputed question of construction or interpretation arising
under the Plan shall be final, binding, and conclusive upon all persons.

III. ELIGIBILITY.

         3.1 Eligibility Requirements. The Committee may from time to time
establish eligibility requirements for Employees to participate in the Plan.



                                      -2-
<PAGE>   3


         3.2 Designation of Participants. From time to time during the
continuation of the Plan, the Committee may designate one or more eligible
Employees to participate in the Plan and shall advise each such Employee of his
selection.

IV. SUPPLEMENTAL DISABILITY PAYMENTS.

         4.1 Monthly Disability Benefit. A Participant who has been found by the
Committee, upon the advice of physicians of its selection, to have a total and
permanent disability shall be entitled to receive a monthly supplemental
disability benefit, commencing on the first day of the month following the
Committee's determination of such disability and continuing until the
Participant attains his Normal Retirement Date or dies, in an amount equal to
the excess of 60% of the Participant's monthly salary at the time of his
disability, over the total of the monthly amounts payable to the Participant
during each applicable month under the Retirement Plan, the U.S. Social Security
Act, and the Short-Term Disability Plan and Long-Term Disability Plan of the
Company, and under any retirement or disability plan or program of a former
employer.

         4.2 Withholding of Taxes. The Company shall deduct from the amount of
all benefits paid to disabled Participants under the Plan any taxes required to
be withheld by the Federal or any state or local government.

V. RIGHTS OF PARTICIPANTS.

         5.1 Limitation of Rights. Nothing in this Plan shall be construed to:

                  (a) Give any Employee of the Company or a Subsidiary any right
         to participate in this Plan; or

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

                  (c) Give a Participant any interest in any fund or in any
         specific asset or assets of the Company or any Subsidiary; or

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

         5.2 Nonalienation of Benefits. No right or benefit under this Plan
shall be subject to anticipation, alienation, sale, assignment, pledge,
encumbrance or charge of any nature, 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.



                                      -3-
<PAGE>   4


         5.3 Prerequisites to Benefits. No Participant shall have any right or
interest in the Plan, or any benefits hereunder, unless and until all the terms,
conditions and provisions of the Plan which affect such Participant shall have
been complied with as specified herein.

VI. MISCELLANEOUS.

         6.1 Amendment or Termination of the Plan. The Board may amend or
terminate this Plan at any time. Any such amendment or termination shall not,
however, affect the rights of any Participant who has commenced receiving
benefits hereunder.

         6.2 Reliance upon Information. The Board and the Committee shall 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 such decision or action taken by the Board or the Committee in reliance upon
any information supplied to them by an officer of the Company, the Company's
legal counsel or by the Company's independent accountants in connection with the
administration of this Plan shall be deemed to have been taken in good faith.

         6.3 Applicable Laws. This Plan shall be construed, administered and
governed in all respects under the laws of the State of Texas.

                                                   PENNZOIL-QUAKER STATE COMPANY


                                      -4-