GENERAL CALIFORNIA MUNICIPAL BOND FUND INC /NY/
497, 2000-03-06
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                                                                 March 10, 2000

                 GENERAL CALIFORNIA MUNICIPAL BOND FUND, INC.

                           SUPPLEMENT TO PROSPECTUS
                            DATED FEBRUARY 1, 2000

THE FOLLOWING INFORMATION SUPPLEMENTS OR REPLACES ANY CONTRARY INFORMATION
CONTAINED IN THE FUND'S PROSPECTUS:

     Shares  acquired by purchase or exchange after May 9, 2000, and redeemed or
exchanged  less than 30 days  after  they are  acquired,  will be  subject  to a
redemption  fee of 0.10% of the value of the shares  redeemed or exchanged.  The
redemption  fee will be  retained by the Fund and used  primarily  to offset the
transaction  costs  that  short-term   trading  imposes  on  the  Fund  and  its
shareholders.  For purposes of calculating the 30 day holding  period,  the Fund
will employ the "first in,  first out"  method,  which  assumes  that the shares
redeemed or exchanged are the ones held the longest.

      No  redemption fee will be charged on the redemption or exchange of shares
(1)  through the Fund's Check Redemption Privilege, Automatic Withdrawal Plan or
Dreyfus  Auto-Exchange Privilege, (2) through accounts that are reflected on the
records  of  the  Transfer Agent as omnibus accounts approved by Dreyfus Service
Corporation,  (3)  through  accounts established by securities dealers, banks or
other  financial  institutions  approved  by  Dreyfus  Service  Corporation that
utilize the National Securities Clearing Corporation's networking system, or (4)
acquired  through  the reinvestment of dividends or capital gains distributions.
The  redemption  fee  may  be  waived,  modified  or  terminated  at  any  time.

                                                                       131s0300



                                              March 10, 2000



                 GENERAL CALIFORNIA MUNICIPAL BOND FUND, INC.

               Supplement to Statement of Additional Information
                             Dated February 1, 2000

     The following information  supplements or replaces any contrary information
contained  in the  section of the Fund's  Statement  of  Additional  Information
entitled "How to Redeem Shares":

     Shares  acquired by purchase or exchange after May 9, 2000, and redeemed or
exchanged  less than 30 days  after  they are  acquired,  will be  subject  to a
redemption  fee of 0.10% of the value of the shares  redeemed or exchanged.  The
redemption  fee will be  retained by the Fund and used  primarily  to offset the
transaction  costs  that  short-term   trading  imposes  on  the  Fund  and  its
shareholders.  For purposes of calculating the 30 day holding  period,  the Fund
will employ the "first in,  first out"  method,  which  assumes  that the shares
redeemed or exchanged are the ones held the longest.

     No redemption  fee will be charged on the  redemption or exchange of shares
(1) through the Fund's Check Redemption Privilege,  Automatic Withdrawal Plan or
Dreyfus Auto-Exchange  Privilege, (2) through accounts that are reflected on the
records of the Transfer Agent as omnibus  accounts  approved by Dreyfus  Service
Corporation,  (3) through accounts  established by securities dealers,  banks or
other  financial  institutions  approved  by Dreyfus  Service  Corporation  that
utilize the National Securities Clearing Corporation's networking system, or (4)
acquired through the  reinvestment of dividends or capital gains  distributions.
The redemption fee may be waived, modified or terminated at any time.



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