DREYFUS PREMIER STATE MUNICIPAL BOND FUND
497, 2000-06-01
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                                                                    June 1, 2000

                   DREYFUS PREMIER STATE MUNICIPAL BOND FUND

                           SUPPLEMENT TO PROSPECTUS

                            DATED SEPTEMBER 1, 1999

      THE  FOLLOWING  INFORMATION  SUPPLEMENTS  THE INFORMATION CONTAINED IN THE
SECTION  OF THE FUND'S PROSPECTUS ENTITLED "YOUR INVESTMENT -- SERVICES FOR FUND
INVESTORS."

Class B Shares - Dreyfus Automatic Withdrawal Plan

      For  any  Fund  account  opened on or after July 24, 2000, or any existing
Fund  account to which the Dreyfus Automatic Withdrawal Plan ("AWP") is added on
or  after  July  24,  2000,  there  will  be  no CDSC on Class B shares redeemed
pursuant  to an AWP withdrawal, as long as the amount of the withdrawal does not
exceed  an annual rate of 12% of the greater of the account value at the time of
the  first  withdrawal  under  the  AWP, or the account value at the time of the
subsequent    withdrawal.

                                                                     PSTMBs0600



                                                                  June 1, 2000


                  DREYFUS PREMIER STATE MUNICIPAL BOND FUND

              Supplement to Statement of Additional Information
                             Dated September 1, 1999


      The following information supplements the information contained in the
section of the Fund's Statement of Additional Information entitled "Shareholder
Services - Automatic Withdrawal Plan."

      Class B Shares - Automatic Withdrawal Plan

      For any Fund account opened on or after July 24, 2000, or any existing
Fund account to which the Automatic Withdrawal Plan ("AWP") is added on or after
July 24, 2000, there will be no CDSC on Class B shares redeemed pursuant to an
AWP withdrawal, as long as the amount of the withdrawal does not exceed an
annual rate of 12% of the greater of the account value at the time of the first
withdrawal under the AWP, or the account value at the time of the subsequent
withdrawal. Withdrawals with respect to Class B shares under the AWP that exceed
such amounts will be subject to a CDSC.







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