Exhibit 32.1 to 2005 10-Q

CERTIFICATION OF PERIODIC FINANCIAL REPORT BY CHIEF EXECUTIVE OFFICER PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Form 10-Q for the quarter ended March 31, 2005 of Convergys Corporation (the “Company”), as filed with the Securities and Exchange Commission on May 5, 2005 (the “Report”), I, James F. Orr, President and Chief Executive Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(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.

/s/ James F. Orr

James F. Orr

President and Chief Executive Officer

May 5, 2005

A signed original of this written statement required by Section 906 has been provided to Convergys Corporation and will be retained by Convergys Corporation and furnished to the Securities and Exchange Commission or its staff upon request.