BRINSON FUNDS INC
497, 1998-06-29
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<PAGE>
 
                        THE BRINSON FUNDS (the "Trust")
                                        
                         SUPPLEMENT TO THE PROSPECTUS
                    FOR THE BRINSON FUND -- CLASS I SHARES

                      Prospectus Dated February 11, 1998
                                        


The following information supplements and supersedes any contrary information
contained in the Trust's Prospectus.  Please be sure to retain this supplement
with your Prospectus.

Add the following four sentences immediately after the sixth sentence in the
first paragraph of the section titled "Management of the Trust -- The Advisor":

     Effective on June 29, 1998, Swiss Bank and Union Bank of Switzerland
     merged.  The merger did not result in a change of control or assignment
     and, therefore, did not result in a termination of the investment advisory
     agreements between Brinson Partners and the Trust, on behalf of each
     Series.  The resulting entity is named UBS AG.  After the merger, Brinson
     Partners will continue its role as investment advisor to the Trust as part
     of the UBS Brinson Division of UBS AG.



This supplement is dated June 29, 1998.
<PAGE>
 
                        THE BRINSON FUNDS (the "Trust")
                                        
                         SUPPLEMENT TO THE PROSPECTUS
                    FOR THE BRINSON FUND -- CLASS N SHARES

                      Prospectus Dated February 11, 1998
                                        


The following information supplements and supersedes any contrary information
contained in the Trust's Prospectus.  Please be sure to retain this supplement
with your Prospectus.

Add the following four sentences immediately after the sixth sentence in the
first paragraph of the section titled "Management of the Trust -- The Advisor":

     Effective on June 29, 1998, Swiss Bank and Union Bank of Switzerland
     merged.  The merger did not result in a change of control or assignment
     and, therefore, did not result in a termination of the investment advisory
     agreements between Brinson Partners and the Trust, on behalf of each
     Series.  The resulting entity is named UBS AG.  After the merger, Brinson
     Partners will continue its role as investment advisor to the Trust as part
     of the UBS Brinson Division of UBS AG.



This supplement is dated June 29, 1998.
<PAGE>
 
                                        
SWISSKEY GLOBAL FUND                       SWISSKEY U.S. EQUITY FUND
SWISSKEY GLOBAL EQUITY FUND                SWISSKEY U.S. LARGE
SWISSKEY GLOBAL BOND FUND                   CAPITALIZATION EQUITY FUND
SWISSKEY U.S. BALANCED FUND                SWISSKEY U.S. BOND FUND
                                           SWISSKEY NON-U.S. EQUITY FUND

                Supplement to Prospectus Dated February 11, 1998
                                        


The following information supplements and supersedes any contrary information
contained in the Trust's Prospectus.  Please be sure to retain this supplement
with your Prospectus.

Add the following four sentences immediately after the sixth sentence in the
first paragraph of the section titled "Management of the Trust -- The Advisor":

     Effective on June 29, 1998, Swiss Bank and Union Bank of Switzerland
     merged.  The merger did not result in a change of control or assignment
     and, therefore, did not result in a termination of the investment advisory
     agreements between Brinson Partners and the Trust, on behalf of each
     Series.  The resulting entity is named UBS AG.  After the merger, Brinson
     Partners will continue its role as investment advisor to the Trust as part
     of the UBS Brinson Division of UBS AG.



This supplement is dated June 29, 1998.
<PAGE>
 
                        THE BRINSON FUNDS (the "Trust")

                                  GLOBAL FUND
                              GLOBAL EQUITY FUND
                               GLOBAL BOND FUND
                              U.S. BALANCED FUND
                               U.S. EQUITY FUND
                     U.S. LARGE CAPITALIZATION EQUITY FUND
                                U.S. BOND FUND
                             NON-U.S. EQUITY FUND

   Supplement to Statement of Additional Information dated February 11, 1998

The following information supplements and supersedes any contrary information
contained in the Trust's Statement of Additional Information.  Please be sure to
retain this supplement with your Statement of Additional Information.

Add the following three sentences immediately after the sixth sentence in the 
first paragraph of the section titled "Investment Advisory and Other Services --
Advisor".

     Effective on June 29, 1998, Swiss Bank and Union Bank of Switzerland
     merged. The resulting entity is named UBS AG. After the merger, Brinson
     Partners will continue its role as investment advisor to the Trust as part
     of the UBS Brinson Division of UBS AG.


This supplement is dated June 29, 1998.


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