SALOMON BROTHERS VARIABLE SERIES FUNDS INC
497, 1998-06-17
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<PAGE>
 
                   SALOMON BROTHERS VARIABLE SERIES FUNDS INC
                              7 WORLD TRADE CENTER
                            NEW YORK, NEW YORK 10048
                                 (888) 777-0102
 
                       Supplement dated June 16, 1998 to
                        Prospectus dated April 10, 1998
 
  The following information supplements should be read in conjunction with the
information contained on the cover page of the Prospectus:
 
  MUTUAL FUND SHARES ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR
ENDORSED BY, ANY BANK, AND ARE NOT FEDERALLY INSURED BY THE FEDERAL DEPOSIT
INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD, OR ANY OTHER AGENCY. MUTUAL
FUND SHARES INVOLVE CERTAIN INVESTMENT RISKS, INCLUDING THE POSSIBLE LOSS OF
PRINCIPAL. THE NET ASSET VALUE OF FUNDS OF THIS TYPE WILL FLUCTUATE FROM TIME
TO TIME.
 
  The following information supplements and should be read in conjunction with
the information contained under the caption "Investment Manager" in the section
of the Series' current Prospectus entitled "Management:"
 
  Roger Lavan is primarily responsible for the day-to-day management of the
  Variable U.S. Government Income Fund and the U.S. investment grade and
  asset allocation portions of the Variable Strategic Bond Fund.


4107701/DW
<PAGE>
 
                   SALOMON BROTHERS VARIABLE SERIES FUNDS INC
                              7 WORLD TRADE CENTER
                            NEW YORK, NEW YORK 10048
                                 (888) 777-0102
 
                  Supplement Dated June 16, 1998 to Prospectus
                             Dated January 2, 1998
 
  The following information supplements and should be read in conjunction with
the information contained on the cover page of the Prospectus:
 
  MUTUAL FUND SHARES ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR
ENDORSED BY, ANY BANK, AND ARE NOT FEDERALLY INSURED BY THE FEDERAL DEPOSIT
INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD, OR ANY OTHER AGENCY. MUTUAL
FUND SHARES INVOLVE CERTAIN INVESTMENT RISKS, INCLUDING THE POSSIBLE LOSS OF
PRINCIPAL. THE NET ASSET VALUE OF FUNDS OF THIS TYPE WILL FLUCTUATE FROM TIME
TO TIME.
 
  The following information supplements and should be read in conjunction with
the information contained under the caption "Investment Manager" in the section
of the Series' current Prospectus entitled "Management:"
 
  Roger Lavan is primarily responsible for the day-to-day management of the
  Variable U.S. Government Income Fund and the U.S. investment grade and
  asset allocation portions of the Variable Strategic Bond Fund.


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