STRONG MONEY MARKET FUND INC
24F-2NT, 1999-01-28
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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:	
	"STRONG MONEY MARKET FUND, INC."	
	100 Heritage Reserve	
	"Menomonee Falls, Wisconsin 53051"	
		
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):    [   ]"	
		
			
3.	Investment Company Act File Number:		
	811-4374		
	Securities Act File Number:		
	2-99439		
			
4.	(a)  Last day of fiscal year for which this Form is filed:		
	10/31/98		
			
	"(b)  Check box if this Form is being filed late (ie., more than 90 calendar
	days after the end of the issuer's fiscal year).  (See Instruction A.2)		
	[    ]		
			
	(c)  Check box if this is the last time the issuer will be filing this Form.		
	[    ]		
			
5.	Calculation of registration fee:		
	(i)  Aggregate sale price of securities sold during the fiscal year		
	pursuant to section 24(f):		"$3,288,849,809.21 "
			
	(ii)  Aggregate price of securities redeemed or repurchased during the		
	fiscal year:		"$3,203,403,721.22 "
			
	(iii)  Aggregate price of securities redeemed or repurchased during		
	"any prior fiscal year ending no earlier than October 11, 1995 that were"		
	not previously used to reduce registration fees payable to the		
	Commission:		"$110,883,682.16 "
			
	(iv)  Total available redemption credits [add items 5(ii) and 5(iii)]:	
     	"$3,314,287,403.38 "
			
	(v)  Net sales - if item 5(i) is greater than item 5(iv)		
	       [subtract item 5(iv) from item 5(i)]:		$0.00 
			
	(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)]:		"($25,437,594.17)"
			
	(vii)  Multiplier for determining registration fee (see instruction C.9):	
       	.000278
			
	(viii)  Registration fee due [multiply item 5(v) by item 5(vii)]		
	"         (enter ""0"" if no fee is due):"		$0.00 
			
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 [effective date of rescisison of rule
 24e-2],"	then report the amount of securities (number of shares or other
 units)  deducted here: 0.  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:  0."		
			
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):		$0.00 
			
8.	Total of the amount of the registration fee due plus any interest due		
	[line 5(viii) plus line 7]:		$0.00 
			
9.	Date the registration fee and any interest payment was sent to the 		
	Commission's lockbox depository:		
	1/21/99		
			
	Method of delivery:		
	[X]  Wire transfer		
	[   ]  Mail or other means		
			
			
			
			

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

	By (Signature and Title)*		
	"/s/ Dana J. Russart, Treasurer"		
	"Dana J. Russart, Treasurer"		
	Date:  1/28/99		
	* Please print the name and title of the signing officer below the signature.		






				
				
				



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