INVESCO MONEY MARKET FUNDS INC
24F-2NT, 1998-08-28
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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.    The name of each  series or class of  securities  for  which  this Form is
      filed (if the form is being filed for all series and classes of securities
      of the issuer, check the box but do not list series or classes):

               x
               -

3.    Investment Company Act File Number:             811-2606

      Securities Act File Number:               2-55079

4(a)  Last day of fiscal year for which this Form is filed:         May 31, 1998

4(b)  ____   Check box if this Form is being filed late (i.e., more than 90 
             calendar days after the end of the issuer's fiscal year).  
             (See Instruction A.2)

4(c)  ____   Check box if this is the last time the issuer will be filing this 
             Form.

5.    Calculation of registration fee:

      (i)   Aggregate sales price of securities
            sold during the fiscal year
            pursuant to section 24(f)           $7,385,291,883
                                                --------------

      (ii)  Aggregate price of securities
            redeemed or repurchased during
            the fiscal year:                    $7,265,578,711
                                                --------------

      (iii) Aggregate  price of securities  
            redeemed or repurchased during 
            any prior fiscal year ending no 
            earlier than October 1, 1995 that 
            were not  previously used to reduce  
            registration fees payable to the
            Commission                          $0
                                                --

      (iv)  Total available redemption credits
            [add items 5(ii) and 5(iii)]        $7,265,578,711
                                                --------------
      (v)   Net sales - if item 5(i) is greater
            than item 5(iv) [subtract item 5(iv) 
            from item 5(i)]                     $119,713,172
                                                ------------
<PAGE>


      (vi)  Redemption  credits available for 
            use in future years - if item 5(i)
            is less than item 5(iv) [subtract 
            item 5(iv) from item 5(i)]          $0
                                                --

      (vii) Multiplier for determining
            registration fee 
            (See Instruction C.9)               x0.000295
                                                --------- 
      (viii)Registration fee due 
            [multiply item 5(v)
            by item 5(vii)] (enter "0" 
            if no fee is due):                  = $35,315.39
                                                ------------
6.    Prepaid Shares

      If the  response  to item 5(i) was  determined  by deducting  an amount of
      securities that were  registered under the Securities Act of 1933 pursuant
      to rule 24e-2 as in effect before October 11, 1997, then report the amount
      of   securities   (number  of  shares  or  other units)   deducted   here:
      _______________.  If there is a number of shares or other units  that were
      registered pursuant to rule 24e-2 remaining unsold at the end of the 
      fiscal year for which this form is filed that are available for use by the
      issuer in future fiscal years, then state that number here: ____________.

7.    Interest due - if this Form is being filed more than 90 days after the end
      of the Issuer's fiscal year (see instruction D) : +$0 
                                                        ---

8.    Total  of  the  amount  of  the registration fee due plus any interest due
      [line 5(viii) plus line 7]: =$35,315.39 
                                   ----------

9.    Date of the registration  fee and any  interest  payment  was  sent to the
      Commission's lockbox depository:

            Method of Delivery:
                              _x_   Wire Transfer
                              ___   Mail or other means


<PAGE>



                                  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 U.S. Government Money Fund



                              By:/s/ Mark H. Williamson
                                 ---------------------- 
                                     Mark H. Williamson
                                     President


Date:         August 27, 1998







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