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                                                                   EXHIBIT 10.13



                   [PENNZOIL-QUAKER STATE COMPANY LETTERHEAD]




                                                                     May 4, 2000



Mr. James L. Pate
Chairman and CEO
Pennzoil-Quaker State Company
P. O. Box 2967
Houston, Texas  77252-2967

Dear Jim:

                  We propose the following Agreement to be effective as of May
4, 2000, for the three years commencing January 1, 2001, which is the day after
the termination of your employment with Pennzoil-Quaker State Company.

                  In consideration of the mutual promises and understanding
contained in this Agreement, you and Pennzoil-Quaker State Company agree as
follows:

         1.       The term of this Agreement shall be three years from January
                  1, 2001.

         2.       Office and secretarial support will be furnished in Houston in
                  accordance with the policy attached hereto as Exhibit A.

         3.       During the term of this Agreement, you will not, without the
                  prior written consent of Pennzoil-Quaker State Company, engage
                  directly or indirectly in any business or endeavor
                  (financially as an individual, investor or lenders or as an
                  employee, director, officer, partner, independent contractor,
                  consultant or owner or in any other capacity calling for the
                  rendition of personal services or acts of management,
                  operation or control) which is in competition or inconsistent
                  with, or adverse to or opposed to, the interests of
                  Pennzoil-Quaker State Company. You should contact the Chief
                  Executive Officer of Pennzoil-Quaker State Company to request
                  such written consent prior to determining it is appropriate to
                  engage in any particular business or endeavor. Notwithstanding
                  the above, you are not prohibited from investing or trading on
                  your own behalf in publicly traded securities of other
                  companies.



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Mr. James L. Pate                          -2-                       May 4, 2000

         4.       During the term of this Agreement, Pennzoil-Quaker State
                  Company will pay you a total of $2,100,000 on a payment
                  schedule as follows: payment will be made in equal monthly
                  amounts of $58,333.33 (except that the last payment shall be
                  $58,333.45) on the first day of the month, commencing January
                  1, 2001, and continuing each month thereafter with the last
                  payment payable on the first day of December, 2003. In
                  addition, Pennzoil-Quaker State Company will reimburse you for
                  all reasonable and necessary travel expenses incurred in
                  performing services for Pennzoil-Quaker State Company in
                  accordance with the policy set forth in Exhibit A. In the
                  event of your death or disability after December 31, 2000, any
                  amount unpaid under the terms hereof shall be paid to your
                  spouse, if living, or to your estate, on the same terms as
                  provided hereunder for payment, or, in the sole discretion of
                  the Board of Directors of Pennzoil-Quaker State Company, at
                  such earlier date as determined by the Board of Directors of
                  Pennzoil-Quaker State Company.

         5.       Neither you, nor your spouse or other beneficiaries shall have
                  the right to assign any part of your or their rights under
                  this Agreement. This Agreement contains the entire
                  understanding between Pennzoil-Quaker State Company and you
                  regarding this matter and supersedes any prior agreement
                  between the parties.

         6.       This Agreement may not be changed or otherwise amended except
                  by mutual consent evidenced in writing and executed by both
                  parties to this Agreement.

         7.       This Agreement is governed by the laws of the State of Texas.

                                                   Very truly yours,


                                                   /s/ JAMES J. POSTL
                                                   -----------------------------
                                                   James J. Postl
                                                   President
                                                   Pennzoil-Quaker State Company


Accepted and agreed to as of the 4th day of May, 2000.


/s/ JAMES L. PATE
-------------------------
James L. Pate


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                                                                       EXHIBIT A


                              SUPPORT AND EXPENSES


                  The following are policies with respect to support and
expenses of Mr. Pate during the three-year period commencing January 1, 2001:

         1.       Company cars and aircraft may be utilized, with any personal
                  use of aircraft subject to IRS imputed income requirements.

         2.       Expenses incurred by Mr. Pate in furtherance of the Company's
                  business shall be reimbursed in accordance with customary
                  Company practices and procedures regarding expense
                  reimbursements.

                  The following are existing Company policies with respect to
retired chief executive officers and will continue throughout Mr. Pate's
retirement:

         1.       Office space, furniture and equipment appropriate to the
                  status of a retired chairman of the board of a publicly-held
                  company will be provided.

         2.       Company will employ an executive assistant, acceptable to Mr.
                  Pate, who will be an employee of the Company with full
                  participation in the Company's employee benefit plans,
                  programs and practices. The executive assistant will report to
                  Mr. Pate and the duties and compensation of that assistant
                  will be determined by Mr. Pate (within the parameters of
                  overall Company guidelines and policy).

         3.       Mr. Pate and his executive assistant will be provided with
                  parking spaces acceptable to Mr. Pate.

         4.       Full reimbursement for cost of private ground transportation
                  service used in lieu of a Company chauffeured car.