STRONG MONEY MARKET FUND INC
497, 1998-08-03
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           PLEASE FILE THIS PROSPECTUS SUPPLEMENT WITH YOUR RECORDS.            


                           STRONG HERITAGE MONEY FUND                           
                            STRONG MONEY MARKET FUND                            
                       STRONG MUNICIPAL MONEY MARKET FUND                       
                            STRONG STEP 1 MONEY FUND                            
                             STRONG ADVANTAGE FUND                              
                        STRONG MUNICIPAL ADVANTAGE FUND                         

                Supplement to the Prospectus dated July 1, 1998                 


STRONG HERITAGE MONEY FUND                                                      

The Strong Heritage Money Fund (the "Fund") now offers the following purchase   
and redemption features.  While these features are primarily designed for       
institutional investors that conduct fund transactions through the federal wire 
system, any shareholder with an account balance of at least $5 million may use  
these features.  The Fund may modify, terminate, or suspend these features
at any time.

SAME-DAY DIVIDEND.  Shareholders of the Fund with account balances of $5        
million or greater who have completed the appropriate documentation will        
receive a dividend on the day of a purchase transaction (a "Same-Day Dividend") 
if the transaction is conducted in accordance with the following procedures.    
Shareholders who have an account balance of less than $5 million but whose      
purchase transaction would increase the account balance to $5 million or        
greater may also receive a Same-Day Dividend.                                   

To receive a Same-Day Dividend, you must place an irrevocable purchase order by 
calling 1-800-733-2274 before 9:00 a.m. Central Time ("CT").  Payment by        
federal funds must be received by Firstar Bank Milwaukee, N.A., the Fund's      
agent, by 2:30 p.m. CT that day.  Any failure to deliver payment by such        
deadline may result in cancellation of the order or liability for the resulting 
interest expense.  Payment for the purchase must be wired as follows:           

     Firstar Bank Milwaukee, N.A.
     777 East Wisconsin Avenue                                                  
     Milwaukee, WI 53202                                                        
     ABA routing number:  075000022                                             
     Account number:  112737-090                                                
     For further credit to:  (insert your account number and registration)      

SAME-DAY WIRE.  Shareholders of the Fund with account balances of at least $5   
million who have completed the appropriate documentation will receive a         
redemption wire on the day of a redemption transaction (a "Same-Day Wire") if   
the redemption order is placed by calling 1-800-733-2274 by 9:00 a.m. CT.       
Dividends will not be earned on the day of redemption on amounts redeemed with  
a same-day wire.  If you redeem all shares in an account, dividends credited to 
the account since the beginning of the month up to the day of redemption will   
be paid the day after redemption proceeds are paid.                             

STRONG STEP 1 MONEY FUND                                                        

NAME CHANGE.  On July 24, 1998, the Board of Directors of the Strong Step 1     
Money Fund changed the name of the Fund to the Strong Investors Money Fund (the 
"Money Fund").                                                                  

EXTENSION OF FEE WAIVER.  Strong Capital Management, Inc., the Money Fund's     
investment advisor (the "Advisor"), has also agreed to extend its voluntarily   
waiver of the Advisor's management fees and absorption of the Money Fund's      
operating expenses through January 1, 1999.                                     


           The date of this Prospectus Supplement is August 3, 1998.            

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