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                                                                       Exhibit 2
                               AMENDMENT NO. 1 TO
                                RIGHTS AGREEMENT


                 This Amendment No. 1 to Rights Agreement (the "Amendment"),
dated as of April 14, 1998, is entered into by and between Quaker State
Corporation, a Delaware corporation (the "Company"), and Mellon Securities
Trust Company, Rights Agent (the "Rights Agent").

                 WHEREAS, the Company and the Rights Agent have entered into a
Rights Agreement, dated as of September 28, 1995 (the "Agreement");

                 WHEREAS, the Company wishes to amend the Agreement;

                 WHEREAS, Section 26 of the Agreement provides, among other
things, that prior to the Stock Acquisition Time the Company may, by resolution
of its Board of Directors, and the Rights Agent shall, if the Company so
directs, supplement or amend certain provisions of the Agreement without the
approval of any holders of Rights; and

                 WHEREAS, the Board of Directors of the Company has approved
this Amendment and the Company has directed the Rights Agent to amend the
Agreement as provided herein;

                 NOW, THEREFORE, the Company and the Rights Agent hereby amend
the Agreement as follows:

                 1.  Capitalized terms used in this Amendment without
definition shall have the meanings given to them in the Agreement.

                 2.       Section 1(a) of the Agreement is amended to add the
following sentence to the end thereof:

         "Notwithstanding anything in this Agreement to the contrary, neither
         Pennzoil Company, a Delaware corporation ("Pennzoil"), Pennzoil
         Products Company, a Delaware corporation ("Downstream"), nor any
         affiliate or subsidiary of  Pennzoil or Downstream shall be deemed to
         be or become an Acquiring Person as a result of the execution,
         delivery and performance under, or consummation of any one or more
         transactions (each, a "Permitted Event" and collectively, the
         "Permitted Events") contemplated by, the Agreement and Plan of Merger,
         dated as of April 14, 1998, as the same may be amended from time to
         time, by and among Downstream, Pennzoil, Downstream Merger Company, a
         Delaware corporation ("Merger Sub"), and the Company (the "Merger
         Agreement"), pursuant to which Merger Sub will be merged (the
         "Merger") with and into the Company."

                 3.  Section 1(gg) is amended to add the following sentence at
the end thereof:
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         "Notwithstanding anything in this Agreement to the contrary, neither
         the acquisition of beneficial ownership of Capital Stock of the
         Company pursuant to the Merger Agreement or the Merger, the
         consummation of any one or more of the Permitted Events, the first
         public announcement of any such acquisition or Permitted Event, nor
         the communication to the Company of any notice with respect to any
         such acquisition or Permitted Event shall constitute or result in the
         occurrence of the Stock Acquisition Time."

                 4.  Section 3(a) of the Agreement is amended to add the
following sentence immediately after the first sentence thereof:

         "Notwithstanding anything in this Agreement to the contrary, neither
         the acquisition of beneficial ownership of Capital Stock of the
         Company pursuant to the Merger Agreement or the Merger nor the
         consummation of any one or more of the Permitted Events shall
         constitute or, with the passage of time, result in the occurrence of a
         Distribution Date."

                 5.  Section 7(a) of the Agreement is amended by (a) deleting
the word "or" at the end of clause (iii) thereto, and (b) adding the following
language immediately following clause (iv) thereof and prior to the
parenthetical:

                 "or (v) immediately prior to the Effective Time, as such term
is defined in the Merger Agreement"

                 6.  Section 11(a)(ii) of the Agreement is amended to add the
following at the end of the first sentence thereof immediately prior to the
period:

         "; provided, however, that, notwithstanding anything in this Agreement
         to the contrary, neither the acquisition of beneficial ownership of
         Capital Stock of the Company pursuant to the Merger Agreement or the
         Merger nor the consummation of any one or more of the Permitted Events
         shall constitute or result in the occurrence of a Section 11(a)(ii)
         Event or any other event set forth in this Section 11(a)(ii) as
         contemplated in Section 24(b)."

                 7.  Section 13(a) of the Agreement is amended to add the
following at the end of the first sentence thereof immediately prior to the
period:

         "; provided, however, that,  notwithstanding anything in this
         Agreement to the contrary, neither the acquisition of beneficial
         ownership of Capital Stock of the Company pursuant to the Merger
         Agreement or the Merger nor the consummation
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         of any one or more of the Permitted Events shall constitute or result
         in the occurrence of a Section 13 Event or any other event set forth
         in this Section 13(a) as contemplated in Section 24(b)."

                 8.  The term "Agreement" as used in the Agreement shall be
deemed to refer to the Agreement as amended hereby.

                 9.  This Amendment shall be governed by and constructed in
accordance with the laws of the State of Delaware.

                 10.  This Amendment shall be effective as of the date first
above written, and, except as set forth herein, the Agreement shall remain in
full force and effect and shall be otherwise unaffected hereby.

                 11.  This Amendment may be executed in two or more
counterparts, each of which shall be deemed to be an original, but all of which
together shall constitute one and the same instrument.
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                 IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be duly executed as of this 14th day of April, 1998.

                                  QUAKER STATE CORPORATION
                                  
                                  By:          /s/ Conrad A. Conrad           
                                      ---------------------------------------
                                      Name:
                                      Title:
                                  
                                  MELLON SECURITIES  TRUST COMPANY
                                  
                                  
                                  By:         /s/ Robert M. Carney, Jr.      
                                      ---------------------------------------
                                      Name:
                                      Title: