EX-99.906CERT

Section 906 Certifications

                CERTIFICATION PURSUANT TO 18 U.S.C SECTION 1350,
                             AS ADOPTED PURSUANT TO
                 SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

John V. Murphy, Principal Executive Officer, and Brian W. Wixted, Principal
Financial Officer, of Centennial Money Market Trust (the "Registrant"), each
certify to the best of his or her knowledge that:

1.    The Registrant's periodic report on Form N-CSR for the period ended June
      30, 2005 (the "Form N-CSR") fully complies with the requirements of
      Section 15(d) of the Securities Exchange Act of 1934, as amended; and

2.    The information contained in the Form N-CSR fairly presents, in all
      material respects, the financial condition and results of operations of
      the Registrant. This certification is being furnished to the Commission
      solely pursuant to 18 U.S.C. ss. 1350 and is not being filed as part of
      the Form N-CSR filed with the Commission.

Principal Executive Officer              Principal Financial Officer

Centennial Money Market Trust            Centennial Money Market Trust

/s/ John V. Murphy                       /s/ Brian W. Wixted
- --------------------------               ----------------------------------
John V. Murphy                           Brian W. Wixted

Date: August 10, 2005                    Date: August 10, 2005