Exhibit 32

                            THE LUBRIZOL CORPORATION

     Certification of Chief Executive Officer and Chief Financial Officer of
           The Lubrizol Corporation Pursuant to 18 U.S.C. Section 1350


I certify that, to the best of my knowledge and belief, the Quarterly Report on
Form 10-Q of The Lubrizol Corporation for the period ending June 30, 2003:

     (1)  fully complies with the requirements of Section 13(a) or 15(d) of the
          Securities Exchange Act of 1934; and

     (2)  the information contained in the Report fairly presents, in all
          material respects, the financial condition and results of operations
          of The Lubrizol Corporation.

        /s/ William G. Bares
----------------------------
William G. Bares
Chief Executive Officer
August 1, 2003


I certify that, to the best of my knowledge and belief, the Quarterly Report on
Form 10-Q of The Lubrizol Corporation for the period ending June 30, 2003:

     (1)  fully complies with the requirements of Section 13(a) or 15(d) of the
          Securities Exchange Act of 1934; and

     (2)  the information contained in the Report fairly presents, in all
          material respects, the financial condition and results of operations
          of The Lubrizol Corporation.

      /s/ Charles P. Cooley
---------------------------
Charles P. Cooley
Chief Financial Officer
August 1, 2003

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