EXHIBIT 32.1

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

      (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/ James L. Hambrick
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James L. Hambrick
Chief Executive Officer and President
March 2, 2005

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, 2004:

      (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
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Charles P. Cooley
Chief Financial Officer
March 2, 2005