<PAGE> PAGE 1
000 A000000 01/31/96
000 C000000 0000803951
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 CALIFORNIA MUNICIPAL MONEY MARKET FND
001 B000000 811-4871
001 C000000 2129226801
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
012 A000001 DREYFUS TRANSFER, INC.
012 B000001 85-11312
012 C010001 PROVIDENCE
012 C020001 RI
012 C030001 02940
012 C040001 9671
012 A000002 FIRST DATA INVESTOR SERVICES GROUP, INC.
012 B000002 84-0000000
012 C010002 PROVIDENCE
012 C020002 RI
012 C030002 02940
018 000000 Y
019 A000000 Y
019 B000000 162
019 C000000 DREYFUSFAM
022 A000001 GOLDMAN, SACHS & CO.
022 B000001 13-5108880
022 C000001 148519
022 D000001 22900
022 A000002 LEHMAN BROTHERS INC.
022 B000002 13-2518466
022 C000002 112466
022 D000002 38500
022 A000003 HAMBRO RESOURCE DEVELOPMENT INCORPORATED
022 B000003 13-3609023
022 C000003 37400
022 D000003 56100
022 A000004 MERRILL LYNCH, PIERCE, FENNER & SMITH INC.
022 B000004 13-5674085
<PAGE> PAGE 2
022 C000004 33025
022 D000004 24025
022 A000005 SMITH BARNEY INC.
022 B000005 13-1912900
022 C000005 28950
022 D000005 27000
022 A000006 PAINEWEBBER INCORPORATED
022 B000006 13-2638166
022 C000006 25175
022 D000006 29600
022 A000007 BT SECURITIES CORPORATION
022 B000007 13-3131014
022 C000007 0
022 D000007 19400
022 A000008 NEWMAN & ASSOCIATES, INC.
022 B000008 84-0775574
022 C000008 9000
022 D000008 7500
022 A000009 MORGAN STANLEY & CO. INCORPORATED
022 B000009 13-2655998
022 C000009 14000
022 D000009 0
022 A000010 J.P. MORGAN SECURITIES INC.
022 B000010 13-3224016
022 C000010 0
022 D000010 14000
023 C000000 418665
023 D000000 253693
028 A010000 159501
028 A020000 1123
028 A030000 0
028 A040000 143381
028 B010000 112396
028 B020000 1100
028 B030000 0
028 B040000 115394
028 C010000 116822
028 C020000 1131
028 C030000 0
028 C040000 138408
028 D010000 86842
028 D020000 1060
028 D030000 0
028 D040000 95971
028 E010000 110658
028 E020000 1187
028 E030000 0
028 E040000 107994
028 F010000 171093
028 F020000 983
028 F030000 0
<PAGE> PAGE 3
028 F040000 179110
028 G010000 757312
028 G020000 6584
028 G030000 0
028 G040000 780258
028 H000000 0
037 000000 N
038 000000 0
039 000000 N
040 000000 Y
041 000000 Y
042 A000000 0
042 B000000 0
042 C000000 0
042 D000000 0
042 E000000 0
042 F000000 0
042 G000000 0
042 H000000 0
043 000000 0
044 000000 0
049 000000 N
050 000000 N
051 000000 N
052 000000 N
053 A000000 N
062 A000000 Y
062 B000000 0.0
062 C000000 0.0
062 D000000 0.0
062 E000000 102.2
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
063 A000000 0
063 B000000 41.0
064 A000000 Y
064 B000000 N
071 A000000 0
071 B000000 0
071 C000000 0
<PAGE> PAGE 4
071 D000000 0
072 A000000 6
072 B000000 8679
072 C000000 0
072 D000000 0
072 E000000 0
072 F000000 1171
072 G000000 0
072 H000000 0
072 I000000 164
072 J000000 24
072 K000000 0
072 L000000 10
072 M000000 12
072 N000000 9
072 O000000 0
072 P000000 0
072 Q000000 0
072 R000000 17
072 S000000 13
072 T000000 0
072 U000000 0
072 V000000 0
072 W000000 10
072 X000000 1430
072 Y000000 0
072 Z000000 7249
072AA000000 0
072BB000000 7
072CC010000 0
072CC020000 0
072DD010000 7249
072DD020000 0
072EE000000 0
073 A010000 0.0156
073 A020000 0.0136
073 B000000 0.0000
073 C000000 0.0000
074 A000000 607
074 B000000 0
074 C000000 456902
074 D000000 0
074 E000000 0
074 F000000 0
074 G000000 0
074 H000000 0
074 I000000 0
074 J000000 0
074 K000000 0
074 L000000 3216
074 M000000 9
<PAGE> PAGE 5
074 N000000 460734
074 O000000 13350
074 P000000 214
074 Q000000 0
074 R010000 0
074 R020000 0
074 R030000 0
074 R040000 135
074 S000000 0
074 T000000 447035
074 U010000 447189
074 U020000 1
074 V010000 1.00
074 V020000 1.00
074 W000000 0.9999
074 X000000 6548
074 Y000000 0
075 A000000 465719
075 B000000 0
076 000000 0.00
077 A000000 Y
077 I000000 Y
077 Q010000 Y
078 000000 N
SIGNATURE JOHN J. PYBURN
TITLE ASSISTANT TREASURER
<TABLE> <S> <C>
<ARTICLE> 6
<CIK> 0000803951
<NAME> GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
<SERIES>
<NUMBER> 001
<NAME> CLASS A
<MULTIPLIER> 1000
<S> <C>
<PERIOD-TYPE> 6-MOS
<FISCAL-YEAR-END> JUL-31-1996
<PERIOD-END> JAN-31-1996
<INVESTMENTS-AT-COST> 456902
<INVESTMENTS-AT-VALUE> 456902
<RECEIVABLES> 3216
<ASSETS-OTHER> 616
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 460734
<PAYABLE-FOR-SECURITIES> 13350
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 349
<TOTAL-LIABILITIES> 13699
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 447190
<SHARES-COMMON-STOCK> 447189
<SHARES-COMMON-PRIOR> 463552
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (155)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 447034
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 8679
<OTHER-INCOME> 0
<EXPENSES-NET> 1430
<NET-INVESTMENT-INCOME> 7249
<REALIZED-GAINS-CURRENT> (7)
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 7242
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (7249)
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 757311
<NUMBER-OF-SHARES-REDEEMED> (780258)
<SHARES-REINVESTED> 6584
<NET-CHANGE-IN-ASSETS> (16369)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (148)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 1171
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 1430
<AVERAGE-NET-ASSETS> 465719
<PER-SHARE-NAV-BEGIN> 1.00
<PER-SHARE-NII> .016
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (.016)
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 1.00
<EXPENSE-RATIO> .006
<AVG-DEBT-OUTSTANDING> 0
<AVG-DEBT-PER-SHARE> 0
</TABLE>
<TABLE> <S> <C>
<ARTICLE> 6
<CIK> 0000803951
<NAME> GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
<SERIES>
<NUMBER> 002
<NAME> CLASS B
<MULTIPLIER> 1000
<S> <C>
<PERIOD-TYPE> 6-MOS
<FISCAL-YEAR-END> JUL-31-1996
<PERIOD-END> JAN-31-1996
<INVESTMENTS-AT-COST> 456902
<INVESTMENTS-AT-VALUE> 456902
<RECEIVABLES> 3216
<ASSETS-OTHER> 616
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 460734
<PAYABLE-FOR-SECURITIES> 13350
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 349
<TOTAL-LIABILITIES> 13699
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 447190
<SHARES-COMMON-STOCK> 1
<SHARES-COMMON-PRIOR> 0
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (155)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 1
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 8679
<OTHER-INCOME> 0
<EXPENSES-NET> 1430
<NET-INVESTMENT-INCOME> 7249
<REALIZED-GAINS-CURRENT> (7)
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 7242
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 0
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 1
<NUMBER-OF-SHARES-REDEEMED> 0
<SHARES-REINVESTED> 0
<NET-CHANGE-IN-ASSETS> (16369)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (148)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 1171
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 1430
<AVERAGE-NET-ASSETS> 0
<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> .017
<AVG-DEBT-OUTSTANDING> 0
<AVG-DEBT-PER-SHARE> 0
</TABLE>
