February 2, 2007

Dreyfus Appreciation Fund, Inc.
Dreyfus Premier GNMA Fund
Dreyfus Premier Municipal Bond Fund
Dreyfus Premier New York Municipal Bond Fund
Dreyfus Premier State Municipal Bond Fund
Dreyfus Premier Worldwide Growth Fund, Inc.
General California Municipal Money Market Fund
General Government Securities Money Market Funds, Inc.
General Money Market Fund, Inc.
General Municipal Money Market Funds, Inc.
General New York Municipal Bond Fund, Inc.
General New York Municipal Money Market Fund

Supplement to Current Statement of Additional Information 

The Fund’s shareholders elected seven new Board members of the Fund. Each Board member, other than Mr. DiMartino, commenced their term on January 1, 2007. Although Mr. DiMartino has served as a Board member of the Fund since 1995, he previously had not stood for election by Fund shareholders.

Name (Age)	Principal Occupation
Position with Fund	During Past 5 Years	Other Board Memberships and Affiliations
Joseph S. DiMartino (63)	Corporate Director and Trustee	The Muscular Dystrophy Association,
Chairman of the Board		Director
(1995)		Century Business Services, Inc., a provider
		of outsourcing functions for small and
		medium size companies, Director
		The Newark Group, a provider of a
		national market of paper recovery
		facilities, paperboard mills and
		paperboard converting plants, Director
		Sunair Services Corporation, engaging in
		the design, manufacture and sale of high
		frequency systems for long-range voice
		and data communications, as well as
		providing certain outdoor-related
		services to homes and businesses,
		Director

Name (Age)	Principal Occupation
Position with Fund	During Past 5 Years	Other Board Memberships and Affiliations
David W. Burke (70)	Corporate Director and Trustee	John F. Kennedy Library Foundation,
Board Member		Director
(2007)		U.S.S. Constitution Museum, Director
Diane Dunst (67)	President, Huntting House	None
Board Member (2007)	Antiques
Jay I. Meltzer (78)	Physician, Internist and	None
Board Member	Specialist in Clinical
(2007)	Hypertension
	Clinical Professor of Medicine
	at Columbia University &
	College of Physicians and
	Surgeons
	Faculty Associate, Center for
	Bioethics, Columbia
	University
Daniel Rose (77)	Chairman and Chief Executive	Baltic-American Enterprise Fund, Vice
Board Member	Officer of Rose Associates,	Chairman and Director
(2007)	Inc., a New York based real	Harlem Educational Activities Fund, Inc.,
	estate development and	Chairman
	management firm	Housing Committee of the Real Estate
		Board of New York, Inc., Director
Warren B. Rudman (76)	Of Counsel to (from January	Collins & Aikman Corporation, Director
Board Member	1993 to December 31, 2003,	Allied Waste Corporation, Director
(2007)	Partner in) the law firm Paul,	Raytheon Company, Director
	Weiss, Rifkind, Wharton &	Boston Scientific, Director
	Garrison, LLP
Sander Vanocur (78)	President, Old Owl	None
Board Member	Communications
(2007)