November 15, 1997
                         DREYFUS PREMIER STATE
                         MUNICIPAL BOND FUND
                       SUPPLEMENT TO PROSPECTUS
                          DATED JULY 16, 1997

        EFFECTIVE JANUARY 15, 1998, THE FOLLOWING POLICIES WILL BE IN EFFECT
FOR THE FUND:
        ADDITIONAL INFORMATION ABOUT PURCHASES, EXCHANGES AND REDEMPTIONS.
The Fund is intended to be a long-term investment vehicle and is not designed
to provide investors with a means of speculation on short-term market
movements. A pattern of frequent purchases and exchanges can be disruptive to
efficient portfolio management and, consequently, can be detrimental to the
Fund's performance and its shareholders. Accordingly, if the Fund's
management determines that an investor is engaged in excessive trading, the
Fund, with or without prior notice, may temporarily or permanently terminate
the availability of Fund exchanges, or reject in whole or part any purchase
or exchange request, with respect to such investor's account. Such investors
also may be barred from purchasing other funds in the Dreyfus Family of
Funds. Generally, an investor who makes more than four exchanges out of the
Fund during any calendar year (for calendar year 1998, beginning on January
15th) or who makes exchanges that appear to coincide with an active
market-timing strategy may be deemed to be engaged in excessive trading.
Accounts under common ownership or control will be considered as one account
for purposes of determining a pattern of excessive trading. In addition, the
Fund may refuse or restrict purchase or exchange requests by any person or
group if, in the judgment of the Fund's management, the Fund would be unable
to invest the money effectively in accordance with its investment objective
and policies or could otherwise be adversely affected or if the Fund receives
or anticipates receiving simultaneous orders that may significantly affect
the Fund (E.G., amounts equal to 1% or more of the Fund's total assets). If
an exchange request is refused, the Fund will take no other action with
respect to the shares until it receives further instructions from the
investor. The

(CONTINUED ON REVERSE SIDE)
Fund may delay forwarding redemption proceeds for up to seven days if the
investor redeeming shares is engaged in excessive trading or if the amount of
the redemption request otherwise would be disruptive to efficient portfolio
management or would adversely affect the Fund. The Fund's policy on excessive
trading applies to investors who invest in the Fund directly or through
financial intermediaries, but does not apply to the Dreyfus Auto-Exchange
Privilege, to any automatic investment or withdrawal privilege described
herein, or to participants in employer-sponsored retirement plans.
        During times of drastic economic or market conditions, the Fund may
suspend the Exchange Privilege temporarily without notice and treat exchange
requests based on their separate components _ redemption orders with a
simultaneous request to purchase the other fund's shares. In such a case, the
redemption request would be processed at the Fund's next determined net asset
value but the purchase order would be effective only at the net asset value
next determined after the fund being purchased receives the proceeds of the
redemption, which may result in the purchase being delayed.
                                                            PSTEBFs1197