Exhibit 32

Pursuant to 18 U.S.C. Section 1350, as created by Section 906 of the Sarbanes–Oxley Act of 2002, the following certifications are being made to accompany the annual report on Form 10-K for the fiscal year ended July 31, 2004 for Donaldson Company, Inc.:

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

I, William M. Cook, Chief Executive Officer of Donaldson Company, Inc., certify that:

1. The Annual Report on Form 10-K of Donaldson Company, Inc. for the fiscal year ended July 31, 2004 (the “Report”), 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 Donaldson Company, Inc.

Date: October 6, 2004 /s/   William M. Cook      William M. Cook
Chief Executive Officer

CERTIFICATION OF CHIEF FINANCIAL OFFICER

I, Thomas R. VerHage, Chief Financial Officer of Donaldson Company, Inc., certify that:

1. The Annual Report on Form 10-K of Donaldson Company, Inc. for the fiscal year ended July 31, 2004 (the “Report”), 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 Donaldson Company, Inc.

Date: October 6, 2004 /s/   Thomas R. VerHage      Thomas R. VerHage
Chief Financial Officer

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