October 23, 1998


               DREYFUS PREMIER STATE MUNICIPAL BOND FUND

                Supplement to Prospectus Dated August 28, 1998

Small Account Fee

     In order to offset the relatively higher costs of servicing smaller
accounts, the Fund will charge regular accounts with balances below $2,000 an
annual fee of $12.  The valuation of accounts and the deductions are expected to
take place during the last four months of each year.  The fee will be waived for
any investor whose aggregate Dreyfus mutual fund investments total at least
$25,000, and will not apply to IRA accounts or to accounts participating in
automatic investment programs or opened through a securities dealer, bank or
other financial institution, or to other fiduciary accounts.