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, 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
August 4, 2004

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, 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
August 4, 2004