<PAGE> PAGE 1
000 B000000 07/31/96
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 2129226785
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 156
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 LEHMAN BROTHERS INC.
022 B000001 13-2518466
022 C000001 341963
022 D000001 70400
022 A000002 PAINEWEBBER INCORPORATED
022 B000002 13-2638166
022 C000002 114075
022 D000002 162200
022 A000003 HAMBRO RESOURCE DEVELOPMENT INCORPORATED
022 B000003 13-3609023
022 C000003 98500
022 D000003 73900
022 A000004 GOLDMAN, SACHS & CO.
022 B000004 13-5108880
<PAGE> PAGE 2
022 C000004 236032
022 D000004 34900
022 A000005 SMITH BARNEY INC.
022 B000005 13-1912900
022 C000005 96766
022 D000005 68550
022 A000006 MERRILL LYNCH, PIERCE, FENNER & SMITH INC.
022 B000006 13-5674085
022 C000006 64063
022 D000006 38225
022 A000007 BT SECURITIES CORPORATION
022 B000007 13-3131014
022 C000007 10500
022 D000007 30400
022 A000008 J.P. MORGAN SECURITIES INC.
022 B000008 13-3224016
022 C000008 5000
022 D000008 29113
022 A000009 MORGAN STANLEY & CO. INCORPORATED
022 B000009 13-2655998
022 C000009 19000
022 D000009 7000
022 A000010 NEWMAN & ASSOCIATES, INC.
022 B000010 84-0775574
022 C000010 17200
022 D000010 7500
023 C000000 1067452
023 D000000 583153
026 A000000 N
026 B000000 Y
026 C000000 N
026 D000000 Y
026 E000000 N
026 F000000 N
026 G010000 N
026 G020000 N
026 H000000 Y
028 A010000 144428
028 A020000 847
028 A030000 0
028 A040000 146974
028 B010000 136072
028 B020000 891
028 B030000 0
028 B040000 132283
028 C010000 101697
028 C020000 825
028 C030000 0
028 C040000 171247
028 D010000 111915
028 D020000 841
<PAGE> PAGE 3
028 D030000 0
028 D040000 103291
028 E010000 73068
028 E020000 749
028 E030000 0
028 E040000 86892
028 F010000 74361
028 F020000 763
028 F030000 0
028 F040000 57156
028 G010000 641541
028 G020000 4916
028 G030000 0
028 G040000 697843
028 H000000 0
062 A000000 Y
062 B000000 0.0
062 C000000 0.0
062 D000000 0.0
062 E000000 99.2
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 66
063 B000000 0.0
064 A000000 Y
064 B000000 N
066 A000000 N
067 000000 N
068 A000000 N
068 B000000 N
069 000000 N
071 A000000 0
071 B000000 0
071 C000000 0
071 D000000 0
072 A000000 12
072 B000000 15652
072 C000000 0
072 D000000 0
072 E000000 0
<PAGE> PAGE 4
072 F000000 2195
072 G000000 0
072 H000000 0
072 I000000 484
072 J000000 47
072 K000000 0
072 L000000 13
072 M000000 24
072 N000000 19
072 O000000 1
072 P000000 0
072 Q000000 0
072 R000000 42
072 S000000 21
072 T000000 0
072 U000000 0
072 V000000 0
072 W000000 17
072 X000000 2863
072 Y000000 0
072 Z000000 12789
072AA000000 1
072BB000000 26
072CC010000 0
072CC020000 0
072DD010000 12785
072DD020000 4
072EE000000 0
073 A010000 0.0290
073 A020000 0.0253
073 B000000 0.0000
073 C000000 0.0000
074 A000000 1515
074 B000000 0
074 C000000 392631
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 1785
074 M000000 35
074 N000000 395966
074 O000000 0
074 P000000 210
074 Q000000 0
074 R010000 0
074 R020000 0
<PAGE> PAGE 5
074 R030000 0
074 R040000 126
074 S000000 0
074 T000000 395630
074 U010000 390328
074 U020000 5475
074 V010000 1.00
074 V020000 1.00
074 W000000 0.9995
074 X000000 5947
074 Y000000 0
075 A000000 438887
075 B000000 0
076 000000 0.00
077 A000000 Y
077 B000000 Y
080 A000000 NAT'L. UNION FIRE INS. CO. OF PITTSBURGH, PA
080 B000000 VIGILANT INSURANCE COMPANY
080 C000000 125000
081 A000000 Y
081 B000000 172
082 A000000 N
082 B000000 0
083 A000000 N
083 B000000 0
084 A000000 N
084 B000000 0
085 A000000 Y
085 B000000 N
SIGNATURE RICHARD W. INGRAM
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> YEAR
<FISCAL-YEAR-END> JUL-31-1996
<PERIOD-END> JUL-31-1996
<INVESTMENTS-AT-COST> 392631
<INVESTMENTS-AT-VALUE> 392631
<RECEIVABLES> 1785
<ASSETS-OTHER> 1550
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 395966
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 336
<TOTAL-LIABILITIES> 336
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 395803
<SHARES-COMMON-STOCK> 390328
<SHARES-COMMON-PRIOR> 463552
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (173)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 390155
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 15652
<OTHER-INCOME> 0
<EXPENSES-NET> 2863
<NET-INVESTMENT-INCOME> 12789
<REALIZED-GAINS-CURRENT> (25)
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 12764
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (12785)
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 1393368
<NUMBER-OF-SHARES-REDEEMED> (1478087)
<SHARES-REINVESTED> 11496
<NET-CHANGE-IN-ASSETS> (67774)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (148)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 2195
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 2863
<AVERAGE-NET-ASSETS> 438887
<PER-SHARE-NAV-BEGIN> 1.00
<PER-SHARE-NII> .029
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (.029)
<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> 0000803951
<NAME> GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
<SERIES>
<NUMBER> 002
<NAME> CLASS B
<MULTIPLIER> 1000
<S> <C>
<PERIOD-TYPE> YEAR
<FISCAL-YEAR-END> JUL-31-1996
<PERIOD-END> JUL-31-1996
<INVESTMENTS-AT-COST> 392631
<INVESTMENTS-AT-VALUE> 392631
<RECEIVABLES> 1785
<ASSETS-OTHER> 1550
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 395966
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 336
<TOTAL-LIABILITIES> 336
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 395803
<SHARES-COMMON-STOCK> 5475
<SHARES-COMMON-PRIOR> 0
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (173)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 5475
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 15652
<OTHER-INCOME> 0
<EXPENSES-NET> 2863
<NET-INVESTMENT-INCOME> 12789
<REALIZED-GAINS-CURRENT> (25)
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 12764
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (4)
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 5485
<NUMBER-OF-SHARES-REDEEMED> (14)
<SHARES-REINVESTED> 4
<NET-CHANGE-IN-ASSETS> (67774)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (148)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 2195
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 2863
<AVERAGE-NET-ASSETS> 171
<PER-SHARE-NAV-BEGIN> 1.00
<PER-SHARE-NII> .025
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (.025)
<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>
