APAC Customer Services 10-Q 2004 Q2 Quarterly report

Exhibit 32.1

Certification of CEO and CFO 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 Quarterly Report on Form 10-Q of APAC Customer Services, Inc. (the “Company”) for the fiscal quarter ended June 27, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Robert J. Keller, as Chief Executive Officer of the Company, and Marc T. Tanenberg, as Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to his knowledge:

(1) 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(a) 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.

/s/ Robert J. Keller

Name: Robert J. Keller

Title: Chief Executive Officer

Date: August 4, 2004

/s/ Marc T. Tanenberg

Name: Marc T. Tanenberg

Title: Chief Financial Officer

Date: August 4, 2004

This certification accompanies the Report pursuant to § 906 of the Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the Sarbanes-Oxley Act of 2002, be deemed filed by the Company for purposes of §18 of the Securities Exchange Act of 1934, as amended, and is not to be incorporated by reference into any filing of the Company, whether made before or after the date hereof, regardless of any general incorporation language in such filing.