EXHIBIT 11(b)


CERTIFICATION OF SHAREHOLDER REPORT

         In connection with the Certified Shareholder Report of AIM Money Market
Funds, Inc. (Formerly: INVESCO Money Market Funds, Inc.) (the "Company") on Form
N-CSR for the period ended August 31, 2003 as filed with the Securities and
Exchange Commission (the "Report"), I, Robert H. Graham, Principal Executive
Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted
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.

Date: August 3, 2004            /s/ Robert H. Graham
                                ----------------------------------------------
                                Robert H. Graham, Principal Executive Officer

         A signed original of this written statement required by Section 906, or
other document authenticating, acknowledging, or otherwise adopting the
signature that appears in typed form within the electronic version of this
written statement required by Section 906, has been provided to the Company and
will be retained by the Company and furnished to the Securities and Exchange
Commission or its staff upon request.





CERTIFICATION OF SHAREHOLDER REPORT

         In connection with the Certified Shareholder Report of AIM Money Market
Funds, Inc. (Formerly: INVESCO Money Market Funds, Inc.) (the "Company") on Form
N-CSR for the period ended August 31, 2003 as filed with the Securities and
Exchange Commission (the "Report"), I, Sidney M. Dilgren, Principal Financial
Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted
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.

Date: August 3, 2004           /s/ Sidney M. Dilgren
                               -------------------------------------------------
                               Sidney M. Dilgren, Principal Financial Officer

         A signed original of this written statement required by Section 906, or
other document authenticating, acknowledging, or otherwise adopting the
signature that appears in typed form within the electronic version of this
written statement required by Section 906, has been provided to the Company and
will be retained by the Company and furnished to the Securities and Exchange
Commission or its staff upon request.