<PAGE> PAGE 1
000 A000000 05/31/98
000 C000000 0000803950
000 D000000 N
000 E000000 NF
000 F000000 Y
000 G000000 N
000 H000000 N
000 I000000 3.0
000 J000000 U
001 A000000 GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
001 B000000 811-4870
001 C000000 2129226805
002 A000000 200 PARK AVENUE
002 B000000 NEW YORK
002 C000000 NY
002 D010000 10166
003 000000 N
004 000000 N
005 000000 N
006 000000 N
007 A000000 N
007 B000000 0
018 000000 Y
019 A000000 Y
019 B000000 159
019 C000000 DREYFUSFAM
020 C000001 0
020 C000002 0
020 C000003 0
020 C000004 0
020 C000005 0
020 C000006 0
020 C000007 0
020 C000008 0
020 C000009 0
020 C000010 0
021 000000 0
022 A000001 SMITH BARNEY INC.
022 B000001 13-1912900
022 C000001 221850
022 D000001 62167
022 A000002 LEHMAN BROTHERS INC.
022 B000002 13-1912900
022 C000002 40470
022 D000002 35500
022 A000003 CITICORP SECURITIES INC.
022 B000003 13-2771536
022 C000003 42400
022 D000003 25400
022 A000004 BEAR, STEARNS & CO. INC.
022 B000004 13-3299429
<PAGE> PAGE 2
022 C000004 47784
022 D000004 17730
022 A000005 PAINEWEBBER INCORPORATED
022 B000005 13-2638166
022 C000005 47800
022 D000005 3000
022 A000006 GOLDMAN, SACHS & CO.
022 B000006 13-5108880
022 C000006 31945
022 D000006 13800
022 A000007 MERRILL LYNCH, PIERCE, FENNER & SMITH INC.
022 B000007 13-5674085
022 C000007 25425
022 D000007 12100
022 A000008 PRUDENTIAL SECURITIES INCORPORATED
022 B000008 22-2347336
022 C000008 15050
022 D000008 14050
022 A000009 J.P. MORGAN SECURITIES, INC.
022 B000009 13-3224016
022 C000009 19360
022 D000009 9360
022 C000010 0
022 D000010 0
023 C000000 492084
023 D000000 193107
028 A010000 104413
028 A020000 1225
028 A030000 0
028 A040000 112916
028 B010000 136134
028 B020000 1098
028 B030000 0
028 B040000 120501
028 C010000 90766
028 C020000 914
028 C030000 0
028 C040000 97702
028 D010000 93609
028 D020000 998
028 D030000 0
028 D040000 103865
028 E010000 96761
028 E020000 1104
028 E030000 0
028 E040000 119959
028 F010000 104266
028 F020000 1167
028 F030000 0
028 F040000 93815
028 G010000 625949
<PAGE> PAGE 3
028 G020000 6506
028 G030000 0
028 G040000 648758
028 H000000 0
042 A000000 0
042 B000000 0
042 C000000 100
042 D000000 0
042 E000000 0
042 F000000 0
042 G000000 0
042 H000000 0
043 000000 46
044 000000 135
054 A000000 Y
054 B000000 Y
054 C000000 Y
054 D000000 N
054 E000000 N
054 F000000 N
054 G000000 Y
054 H000000 N
054 I000000 N
054 J000000 Y
054 K000000 N
054 L000000 Y
054 M000000 Y
054 N000000 N
054 O000000 Y
055 A000000 Y
055 B000000 N
056 000000 N
057 000000 N
062 A000000 Y
062 B000000 0.0
062 C000000 0.0
062 D000000 0.0
062 E000000 99.4
062 F000000 0.0
062 G000000 0.0
062 H000000 0.0
062 I000000 0.0
062 J000000 0.0
062 K000000 0.0
062 L000000 0.0
062 M000000 0.0
062 N000000 0.0
062 O000000 0.0
062 P000000 0.0
062 Q000000 0.0
062 R000000 0.0
<PAGE> PAGE 4
063 A000000 38
063 B000000 0.0
064 A000000 Y
064 B000000 N
071 A000000 0
071 B000000 0
071 C000000 0
071 D000000 0
072 A000000 6
072 B000000 8485
072 C000000 0
072 D000000 0
072 E000000 0
072 F000000 1195
072 G000000 0
072 H000000 0
072 I000000 446
072 J000000 25
072 K000000 0
072 L000000 10
072 M000000 11
072 N000000 18
072 O000000 1
072 P000000 0
072 Q000000 0
072 R000000 15
072 S000000 9
072 T000000 46
072 U000000 0
072 V000000 0
072 W000000 5
072 X000000 1781
072 Y000000 22
072 Z000000 6726
072AA000000 2
072BB000000 0
072CC010000 0
072CC020000 0
072DD010000 6137
072DD020000 589
072EE000000 0
073 A010000 0.0142
073 A020000 0.0128
073 B000000 0.0000
073 C000000 0.0000
074 A000000 655
074 B000000 0
074 C000000 461287
074 D000000 0
074 E000000 0
074 F000000 0
<PAGE> PAGE 5
074 G000000 0
074 H000000 0
074 I000000 0
074 J000000 1001
074 K000000 0
074 L000000 3902
074 M000000 54
074 N000000 466899
074 O000000 0
074 P000000 197
074 Q000000 0
074 R010000 0
074 R020000 0
074 R030000 0
074 R040000 85
074 S000000 0
074 T000000 466617
074 U010000 424136
074 U020000 42545
074 V010000 1.00
074 V020000 1.00
074 W000000 0.9999
074 X000000 7678
074 Y000000 0
075 A000000 433459
075 B000000 0
076 000000 0.00
077 A000000 N
078 000000 N
SIGNATURE MICHAEL S. PETRUCELLI
TITLE ASSISTANT TREASURER
<TABLE> <S> <C>
<ARTICLE> 6
<CIK> 0000803950
<NAME> GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
<SERIES>
<NUMBER> 001
<NAME> CLASS A
<MULTIPLIER> 1000
<S> <C>
<PERIOD-TYPE> 6-MOS
<FISCAL-YEAR-END> NOV-30-1998
<PERIOD-END> MAY-31-1998
<INVESTMENTS-AT-COST> 461287
<INVESTMENTS-AT-VALUE> 461287
<RECEIVABLES> 4903
<ASSETS-OTHER> 709
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 466899
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 282
<TOTAL-LIABILITIES> 282
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 466682
<SHARES-COMMON-STOCK> 424136
<SHARES-COMMON-PRIOR> 440817
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (64)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 424071
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 8485
<OTHER-INCOME> 0
<EXPENSES-NET> 1759
<NET-INVESTMENT-INCOME> 6726
<REALIZED-GAINS-CURRENT> 2
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 6728
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (6137)
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 573814
<NUMBER-OF-SHARES-REDEEMED> (596414)
<SHARES-REINVESTED> 5920
<NET-CHANGE-IN-ASSETS> (16304)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (66)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 1195
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 1781
<AVERAGE-NET-ASSETS> 433459
<PER-SHARE-NAV-BEGIN> 1.00
<PER-SHARE-NII> .014
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (.014)
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 1.00
<EXPENSE-RATIO> .007
<AVG-DEBT-OUTSTANDING> 0
<AVG-DEBT-PER-SHARE> 0
</TABLE>
<TABLE> <S> <C>
<ARTICLE> 6
<CIK> 0000803950
<NAME> GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
<SERIES>
<NUMBER> 002
<NAME> CLASS B
<MULTIPLIER> 1000
<S> <C>
<PERIOD-TYPE> 6-MOS
<FISCAL-YEAR-END> NOV-30-1998
<PERIOD-END> MAY-31-1998
<INVESTMENTS-AT-COST> 461287
<INVESTMENTS-AT-VALUE> 461287
<RECEIVABLES> 4903
<ASSETS-OTHER> 709
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 466899
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 282
<TOTAL-LIABILITIES> 282
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 466682
<SHARES-COMMON-STOCK> 42545
<SHARES-COMMON-PRIOR> 42169
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (64)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 42546
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 8485
<OTHER-INCOME> 0
<EXPENSES-NET> 1759
<NET-INVESTMENT-INCOME> 6726
<REALIZED-GAINS-CURRENT> 2
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 6728
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (589)
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 52135
<NUMBER-OF-SHARES-REDEEMED> (52344)
<SHARES-REINVESTED> 586
<NET-CHANGE-IN-ASSETS> (16304)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (66)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 1195
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 1781
<AVERAGE-NET-ASSETS> 45945
<PER-SHARE-NAV-BEGIN> 1.00
<PER-SHARE-NII> .013
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (.013)
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 1.00
<EXPENSE-RATIO> .010
<AVG-DEBT-OUTSTANDING> 0
<AVG-DEBT-PER-SHARE> 0
</TABLE>
