<PAGE> PAGE 1
000 A000000 01/31/95
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
011 A000001 PREMIER MUTUAL FUND SERVICES, INC.
011 B000001 8-47312
011 C010001 NEW YORK
011 C020001 NY
011 C030001 10166
013 A000001 ERNST & YOUNG LLP
013 B010001 NEW YORK
013 B020001 NY
013 B030001 10019
018 000000 Y
019 A000000 Y
019 B000000 153
019 C000000 DREYFUSFAM
022 A000001 PAINEWEBBER INCORPORATED
022 B000001 13-2638166
022 C000001 69500
022 D000001 124740
022 A000002 GOLDMAN, SACHS & CO.
022 B000002 13-5108880
022 C000002 135726
022 D000002 24900
022 A000003 HAMBRO RESOURCE DEVELOPMENT INCORPORATED
022 B000003 13-3609023
022 C000003 67200
022 D000003 57600
022 A000004 MERRILL LYNCH, PIERCE, FENNER & SMITH INC.
022 B000004 13-5674085
022 C000004 51850
022 D000004 50100
<PAGE> PAGE 2
022 A000005 BT SECURITIES CORPORATION
022 B000005 13-3131014
022 C000005 15500
022 D000005 42665
022 A000006 PRUDENTIAL SECURITIES INCORPORATED
022 B000006 22-2347336
022 C000006 17400
022 D000006 25905
022 A000007 SMITH BARNEY INC.
022 B000007 13-1912900
022 C000007 20900
022 D000007 18400
022 A000008 NEWMAN & ASSOCIATES, INC.
022 B000008 84-0775574
022 C000008 28460
022 D000008 7500
022 A000009 BANK OF AMERICA NT & SA
022 B000009 94-1687665
022 C000009 750
022 D000009 30045
022 A000010 THE FIRST BOSTON CORPORATION
022 B000010 13-5659485
022 C000010 18950
022 D000010 10950
023 C000000 496771
023 D000000 486802
028 A010000 160447
028 A020000 1424
028 A030000 0
028 A040000 196914
028 B010000 173216
028 B020000 1492
028 B030000 0
028 B040000 191707
028 C010000 143405
028 C020000 1385
028 C030000 0
028 C040000 159944
028 D010000 120461
028 D020000 1402
028 D030000 0
028 D040000 138854
028 E010000 142726
028 E020000 1434
028 E030000 0
028 E040000 236125
028 F010000 169406
028 F020000 1181
028 F030000 0
028 F040000 184272
028 G010000 909661
<PAGE> PAGE 3
028 G020000 8318
028 G030000 0
028 G040000 1107816
028 H000000 0
034 000000 N
035 000000 0
036 B000000 0
037 000000 N
038 000000 0
040 000000 N
041 000000 N
062 A000000 Y
062 B000000 0.0
062 C000000 0.0
062 D000000 0.0
062 E000000 97.4
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
063 A000000 51
063 B000000 0.0
064 A000000 Y
064 B000000 N
070 A010000 Y
070 A020000 N
070 B010000 N
070 B020000 N
070 C010000 N
070 C020000 N
070 D010000 N
070 D020000 N
070 E010000 N
070 E020000 N
070 F010000 N
070 F020000 N
070 G010000 N
070 G020000 N
070 H010000 N
070 H020000 N
070 I010000 N
070 I020000 N
<PAGE> PAGE 4
070 J010000 Y
070 J020000 N
070 K010000 N
070 K020000 N
070 L010000 N
070 L020000 N
070 M010000 N
070 M020000 N
070 N010000 N
070 N020000 N
070 O010000 Y
070 O020000 N
070 P010000 Y
070 P020000 N
070 Q010000 N
070 Q020000 N
070 R010000 N
070 R020000 N
071 A000000 0
071 B000000 0
071 C000000 0
071 D000000 0
072 A000000 6
072 B000000 10493
072 C000000 0
072 D000000 0
072 E000000 0
072 F000000 1544
072 G000000 0
072 H000000 0
072 I000000 259
072 J000000 30
072 K000000 0
072 L000000 14
072 M000000 9
072 N000000 4
072 O000000 0
072 P000000 0
072 Q000000 0
072 R000000 8
072 S000000 10
072 T000000 0
072 U000000 0
072 V000000 0
072 W000000 11
072 X000000 1889
072 Y000000 467
072 Z000000 9071
072AA000000 0
072BB000000 3
072CC010000 0
<PAGE> PAGE 5
072CC020000 0
072DD010000 9071
072DD020000 0
072EE000000 0
073 A010000 0.0149
073 A020000 0.0000
073 B000000 0.0000
073 C000000 0.0000
074 A000000 4371
074 B000000 0
074 C000000 496180
074 D000000 0
074 E000000 0
074 F000000 0
074 G000000 0
074 H000000 0
074 I000000 0
074 J000000 4002
074 K000000 0
074 L000000 4997
074 M000000 47
074 N000000 509597
074 O000000 0
074 P000000 204
074 Q000000 0
074 R010000 0
074 R020000 0
074 R030000 0
074 R040000 127
074 S000000 0
074 T000000 509266
074 U010000 509388
074 U020000 0
074 V010000 1.00
074 V020000 0.00
074 W000000 0.9971
074 X000000 7985
074 Y000000 0
075 A000000 612477
075 B000000 0
076 000000 0.00
077 A000000 Y
077 C000000 Y
077 Q010000 Y
077 Q020000 N
077 Q030000 N
078 000000 N
SIGNATURE FREDERICK C. DEY
TITLE VICE PRESIDENT
<TABLE> <S> <C>
<ARTICLE> 6
<CIK> 0000803951
<NAME> GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND
<MULTIPLIER> 1000
<S> <C>
<PERIOD-TYPE> 6-MOS
<FISCAL-YEAR-END> JUL-31-1995
<PERIOD-END> JAN-31-1995
<INVESTMENTS-AT-COST> 496180
<INVESTMENTS-AT-VALUE> 496180
<RECEIVABLES> 8999
<ASSETS-OTHER> 4418
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 509597
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 331
<TOTAL-LIABILITIES> 331
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 509388
<SHARES-COMMON-STOCK> 509388
<SHARES-COMMON-PRIOR> 699225
<ACCUMULATED-NII-CURRENT> 0
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (122)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 509266
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 10493
<OTHER-INCOME> 0
<EXPENSES-NET> 1422
<NET-INVESTMENT-INCOME> 9071
<REALIZED-GAINS-CURRENT> (3)
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 9068
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 9071
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 909661
<NUMBER-OF-SHARES-REDEEMED> (1107816)
<SHARES-REINVESTED> 8318
<NET-CHANGE-IN-ASSETS> (189839)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (120)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 1544
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 1889
<AVERAGE-NET-ASSETS> 612477
<PER-SHARE-NAV-BEGIN> 1.00
<PER-SHARE-NII> .015
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (.015)
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 1.00
<EXPENSE-RATIO> .005
<AVG-DEBT-OUTSTANDING> 0
<AVG-DEBT-PER-SHARE> 0
</TABLE>
