Exhibit 32.01

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The certification set forth below is being submitted in connection with the amended Annual Report on Form 10-K/A (the “Report”) for the purpose of complying with Rule 13a-14(b) or Rule 15d-14(b) of the Securities Exchange Act of 1934 (the “Exchange Act”) and Section 1350 of Chapter 63 of Title 18 of the United States Code.

Neal C. Hansen, the Chief Executive Officer and Peter E. Kalan, the Chief Financial Officer of CSG Systems International Inc., each certifies that, to the best of his knowledge:

(1) the Report fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act; and

(2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of CSG Systems International, Inc.

November 18, 2004

/s/    NEAL C. HANSEN        

Neal C. Hansen

Chairman and Chief Executive Officer

November 18, 2004

/s/    PETER E. KALAN        

Peter E. Kalan

Executive Vice President and Chief Financial Officer