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 Company’s annual report on Form 10-K for the fiscal year ended July 31, 2003:

CERTIFICATION OF CHIEF EXECUTIVE OFFICER (1)

I, William G. Van Dyke, Chief Executive Officer of Donaldson Company, Inc., certify that, to my knowledge:

1. The Annual Report on Form 10-K of Donaldson Company, Inc. for the fiscal year ended July 31, 2003 (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

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

Date: October 14, 2003 /s/   William G. Van Dyke      Chief Executive Officer

CERTIFICATION OF CHIEF EXECUTIVE OFFICER (1)

I, William M. Cook, Chief Financial Officer of Donaldson Company, Inc., certify that, to my knowledge:

1. The Annual Report on Form 10-K of Donaldson Company, Inc. for the fiscal year ended July 31, 2003 (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

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

Date: October 14, 2003 /s/   William M. Cook      Chief Financial Officer

(1) A signed original of this written statement required by Section 906 has been provided to Donaldson Company, Inc. and will be retained by Donaldson Company, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.