INVESCO MONEY MARKET FUNDS INC
24F-2NT, 1997-07-23
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                    U.S. SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549

                                  FORM 24F-2
                       Annual Notice of Securities Sold
                            Pursuant to Rule 24f-2

1.    Name and address of issuer:

              INVESCO Money Market Funds, Inc.
              7800 E. Union Avenue
              Denver, Colorado 80237

2.    Name of each series or class of funds for which this notice is filed:

              INVESCO Money Market Funds, Inc.
                 INVESCO Cash Reserves Fund
                 INVESCO Tax-Free Money Fund
                 INVESCO US Government Money Fund

3.    Investment Company Act File Number:   811-2606

      Securities Act File Number:  2-55079

4.    Last day of fiscal year for which this notice is filed:

              May 31, 1997

5.    Check box if this  notice is being  filed more than 180 days after the
      close of the issuer's  fiscal year for  purposes of  reporting  securities
      sold after the close of the  fiscal  year but  before  termination  of the
      issuer's 24f-2 declaration:




6.    Date of termination of issuer's declaration under rule 24f-2(a)(1), if 
      applicable (see Instruction A.6):

              Not Applicable

7.    Number and amount of  securities  of the same class or series which had
      been  registered  under the  Securities Act of 1933 other than pursuant to
      Rule  24f-2 in a prior  fiscal  year,  but  which  remained  unsold at the
      beginning of the fiscal year:

                                          0


<PAGE>



8     Number and amount of securities registered during the fiscal year other
      than pursuant to Rule 24f-2:

              Shares =45,646,263      $45,646,263


9.    Number and aggregate sale price of securities sold during the fiscal year:

              Shares =6,934,311,306       $6,934,311,306

10.   Number and aggregate  sale price of securities  sold during the fiscal
      year in reliance upon registration pursuant to Rule 24f- 2:

              Shares =6,888,665,043       $6,888,665,043

11.   Number and  aggregate  sales price of  securities  issued  during the
      fiscal year in connection with dividend  reinvestment plans, if applicable
      (see Instruction B.7):

              N/A

12.   Calculation of registration fee:

      (i)     Aggregate sale price of securities
              sold during the fiscal year in
              reliance on Rule 24f-2
              (from Item 10):                                $  6,888,665,043
                                                             ----------------

      (ii)    Aggregate price of shares issued
              in connection with dividend
              reinvestment plans (from Item 11,
              if applicable):                                +     N/A
                                                             ----------------

      (iii)   Aggregate price of shares redeemed
              or repurchased during the fiscal
              year (if applicable):                          -  6,876,952,034
                                                             ----------------

      (iv)    Aggregate price of shares redeemed 
              or repurchased and previously applied
              as a reduction to filing fees pursuant
              to Rule 24e-2 (if applicable):                 +       N/A
                                                             ----------------

      (v)     Net aggregate price of securities sold
              and issued during the fiscal year in  
              reliance on Rule 24f-2 [line (i),
              plus line (ii), less line (iii), 
              plus line (iv)] if applicable:                 $     11,713,009
                                                             ----------------



<PAGE>


      (vi)    Multiplier prescribed by Section
              6(b) of the Securities Act of 1933
              or other applicable law or regula-
              tion (see Instruction C.6):                    x         1/3300
                                                             ----------------

      (vii)   Fee due [line (i) or line(v)
              multiplied by line (vi)]:                      $       3,549.40
                                                             ================

Instruction:     Issuers should complete lines (ii), (iii), (iv), and
                 (v) only if the form is being filed within 60 days
                 after the close of the issuer's fiscal year.  See
                 Instruction C.3.

13.   Check  box  if  fees  are  being  remitted  to  the  Commission's  lockbox
      depository  as  described  in  Section  3a of the  Commission's  Rules  of
      Information and Other Procedures (17 CFR 202.3a).

                X

Date of mailing or wire  transfer  of filing  fees to the  Commission's  lockbox
depository:

              July 22, 1997



                                  SIGNATURES

This  report has been  signed  below by the  following  persons on behalf of the
issuer and in the capacities and on the date indicated.

                              INVESCO Money Market Funds, Inc.
                                 INVESCO Cash Reserves Fund
                                 INVESCO Tax-Free Money Fund
                                 INVESCO US Government Money Fund


                              By:     /s/ Dan J. Hesser
                                      -----------------
                                      Dan J. Hesser
                                      President

                              Date:   July 22, 1997



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