SECURITY CAPITAL EUROPEAN REAL ESTATE SHARES INC
497, 1998-12-31
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<PAGE>
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
                 SECURITY CAPITAL EUROPEAN REAL ESTATE SHARES

        
                      Supplement dated December 31, 1998
                                      to
Class I Prospectus and Statement of Additional Information dated August 19, 1998

    GCMG HAS COMMITTED TO CONTINUE TO WAIVE FEES AND/OR REIMBURSE EXPENSES
  TO MAINTAIN SC-EURO'S CLASS I OPERATING EXPENSES, OTHER THAN BROKERAGE FEES
      AND COMMISSIONS, TAXES, INTEREST AND OTHER EXTRAORDINARY EXPENSES,
    AT NO MORE THAN 1.45% OF SC-EURO'S CLASS I AVERAGE DAILY NET ASSETS FOR
                      THE YEAR ENDING DECEMBER 31, 1999.

   EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES
    AND SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES WILL NO LONGER BE
     OFFERED AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.
         ACCORDINGLY, SC-EURO CLASS I SHARES MAY NOT BE EXCHANGED FOR
     THE CLASS I SHARES OF SC-ARBITRAGE OR SC-ASIA ON OR AFTER THAT DATE.
<PAGE>
 
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
                 SECURITY CAPITAL EUROPEAN REAL ESTATE SHARES

        
                      Supplement dated December 31, 1998
                                      to
Class R Prospectus and Statement of Additional Information dated August 19, 1998

    GCMG HAS COMMITTED TO CONTINUE TO WAIVE FEES AND/OR REIMBURSE EXPENSES
  TO MAINTAIN SC-EURO'S CLASS R OPERATING EXPENSES, OTHER THAN BROKERAGE FEES
      AND COMMISSIONS, TAXES, INTEREST AND OTHER EXTRAORDINARY EXPENSES,
    AT NO MORE THAN 1.60% OF SC-EURO'S CLASS R AVERAGE DAILY NET ASSETS FOR
                      THE YEAR ENDING DECEMBER 31, 1999.

   EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES
    AND SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES WILL NO LONGER BE
    OFFERED AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.
         ACCORDINGLY, SC-EURO CLASS R SHARES MAY NOT BE EXCHANGED FOR
             THE CLASS R SHARES OF SC-ASIA ON OR AFTER THAT DATE.

<PAGE>
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
               SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES

                      Supplement dated December 31, 1998
                                      to
Class I Prospectus and Statement of Additional Information dated August 19, 1998


  EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES
  AND SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES WILL NO LONGER BE OFFERED
         AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.



<PAGE>
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
               SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES

                      Supplement dated December 31, 1998
                                      to
Class R Prospectus and Statement of Additional Information dated August 19, 1998


  EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES
  AND SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES WILL NO LONGER BE OFFERED
         AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.
 


<PAGE>
 
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
                   SECURITY CAPITAL U.S. REAL ESTATE SHARES

        
                      Supplement dated December 31, 1998
                                      to
Class I Prospectus and Statement of Additional Information dated August 19, 1998

    GCMG HAS COMMITTED THAT BEGINNING JANUARY 1, 1999 THEY WILL WAIVE FEES 
  AND/OR REIMBURSE EXPENSES TO MAINTAIN SC-US'S CLASS R OPERATING EXPENSES, 
     OTHER THAN BROKERAGE FEES AND COMMISSIONS, TAXES, INTEREST AND OTHER 
EXTRAORDINARY EXPENSES, AT NO MORE THAN 1.20% OF SC-US'S CLASS R AVERAGE DAILY 
               NET ASSETS FOR THE YEAR ENDING DECEMBER 31, 1999.
                      

   EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES
    AND SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES WILL NO LONGER BE
     OFFERED AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.
          ACCORDINGLY, SC-US CLASS I SHARES MAY NOT BE EXCHANGED FOR
     THE CLASS I SHARES OF SC-ARBITRAGE OR SC-ASIA ON OR AFTER THAT DATE.

<PAGE>
 
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
                   SECURITY CAPITAL U.S. REAL ESTATE SHARES

        
                      Supplement dated December 31, 1998
                                      to
Class R Prospectus and Statement of Additional Information dated August 19, 1998


    GCMG HAS COMMITTED THAT BEGINNING JANUARY 1, 1999 THEY WILL WAIVE FEES
  AND/OR REIMBURSE EXPENSES TO MAINTAIN SC-US'S CLASS R OPERATING EXPENSES, 
     OTHER THAN BROKERAGE FEES AND COMMISSIONS, TAXES, INTEREST AND OTHER 
EXTRAORDINARY EXPENSES, AT NO MORE THAN 1.35% OF SC-US'S CLASS R AVERAGE DAILY
               NET ASSETS FOR THE YEAR ENDING DECEMBER 31, 1999.
                      

   EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES
    AND SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES WILL NO LONGER BE
     OFFERED AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.
          ACCORDINGLY, SC-US CLASS R SHARES MAY NOT BE EXCHANGED FOR
             THE CLASS R SHARES OF SC-ASIA ON OR AFTER THAT DATE.

 

<PAGE>
 
            SECURITY CAPITAL REAL ESTATE MUTUAL FUNDS INCORPORATED
               SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES

                      Supplement dated December 31, 1998
                                      to
Class I Prospectus and Statement of Additional Information dated August 19, 1998


  EFFECTIVE JANUARY 1, 1999, SECURITY CAPITAL REAL ESTATE ARBITRAGE SHARES
AND SECURITY CAPITAL ASIA/PACIFIC REAL ESTATE SHARES WILL NO LONGER BE OFFERED
         AS INVESTMENT PORTFOLIOS OF SC-REMFS AND WILL BE TERMINATED.
 




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