STRONG MONEY MARKET FUND INC
497, 1999-01-11
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           PLEASE FILE THIS PROSPECTUS SUPPLEMENT WITH YOUR RECORDS.            


                           STRONG HERITAGE MONEY FUND                           
                          STRONG INVESTORS MONEY FUND                           
                            STRONG MONEY MARKET FUND                            
                       STRONG MUNICIPAL MONEY MARKET FUND                       
                             STRONG ADVANTAGE FUND                              
                        STRONG MUNICIPAL ADVANTAGE FUND                         

                Supplement to the Prospectus dated July 1, 1998                 
                      as supplemented on September 8, 1998                      


STRONG ADVANTAGE FUND                                                           

Effective immediately, Mr. Lyle J. Fitterer will cease to be a co-manager of    
the Strong Advantage Fund.  Mr. Thomas A. Sontag joins Mr. Jeffrey A. Koch as a 
co-manager of the Fund.  For thirteen years prior to joining Strong Capital     
Management, Inc., the Fund's investment advisor (the "Advisor"), in November,   
1998, Mr. Sontag worked at Bear Stearns & Co., most recently as a Managing      
Director of the Fixed Income Department.  From September 1982 until December    
1985, Mr. Sontag was employed in the Fixed Income Department at Goldman Sachs & 
Co.  Mr. Sontag received his B.B.A. degree in Economics/Finance from the        
University of Wisconsin-Madison in 1981 and his M.B.A. in Finance from the      
University of Wisconsin-Madison in 1982.                                        

STRONG INVESTORS MONEY FUND                                                     

The Advisor has agreed to voluntarily waive all the Advisor's management fees   
and absorb operating expenses of the Investors Money Fund through April 30,
1999. In addition, the Advisor has agreed to voluntarily waive the Advisor's 
management fee and absorb operating expenses to the extent necessary to 
maintain the Investors Money Fund's operating expenses at no more than 0.35%
from May 1, 1999 through December 31, 1999.

STRONG HERITAGE MONEY FUND                                                      

The Advisor has agreed to extend its voluntary waiver of its fees and/or        
absorptions of fund expenses necessary to maintain the Heritage Money Fund's    
operating expenses at no more than 0.45% through June 30, 1999.                 


          The date of this Prospectus Supplement is January 11, 1999.           

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