THE LUBRIZOL CORPORATION                       Exhibit 32

     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 Annual Report on
Form 10-K of The Lubrizol Corporation for the period ending December 31, 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
February 18, 2004






I certify that, to the best of my knowledge and belief, the Annual Report on
Form 10-K of The Lubrizol Corporation for the period ending December 31, 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
February 18, 2004