Parker-Hannifin (PH) 10-Q 2008 Q3 Quarterly report

Exhibit 32

Certification Pursuant to

18 U.S.C. Section 1350,

As Adopted Pursuant to

§ 906 of the Sarbanes-Oxley Act of 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, in connection with the filing of the Quarterly Report on Form 10-Q of Parker-Hannifin Corporation (the “Company”) for the quarterly period ended March 31, 2008, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned officers of the Company certifies, that, to such officer’s knowledge:

(1) 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 the Company as of the dates and for the periods expressed in the Report.

Dated: May 6, 2008

/s/ Donald E. Washkewicz

Name: Donald E. Washkewicz

Title: Chief Executive Officer

/s/ Timothy K. Pistell

Name: Timothy K. Pistell

Title: Executive Vice President-Finance and

Administration and Chief Financial Officer