<PAGE> PAGE 1
000 A000000 05/31/2000
000 C000000 0000803951
000 D000000 N
000 E000000 NF
000 F000000 Y
000 G000000 N
000 H000000 N
000 I000000 6.1
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
011 A000001 DREYFUS SERVICE CORPORATION
011 B000001 8-13801
011 C010001 NEW YORK
011 C020001 NY
011 C030001 10166
012 A000001 DREYFUS TRANSFER, INC.
012 B000001 85-11312
012 C010001 PROVIDENCE
012 C020001 RI
012 C030001 02940
012 C040001 9671
012 A000002 DELETE
018 000000 Y
019 A000000 Y
019 B000000 175
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 GOLDMAN, SACHS & CO.
022 B000001 13-5108880
<PAGE> PAGE 2
022 C000001 190928
022 D000001 160370
022 A000002 J.P. MORGAN SECURITIES INC.
022 B000002 13-3224016
022 C000002 171204
022 D000002 142985
022 A000003 U.S. BANCORP PIPER JAFFRAY
022 B000003 41-0953246
022 C000003 136716
022 D000003 129205
022 A000004 LEHMAN BROTHERS INC.
022 B000004 13-2518466
022 C000004 133258
022 D000004 82880
022 A000005 PAINEWEBBER INCORPORATED
022 B000005 13-2638166
022 C000005 59400
022 D000005 77755
022 A000006 SALOMON SMITH BARNEY INC.
022 B000006 13-1912900
022 C000006 89460
022 D000006 27650
022 A000007 MORGAN STANLEY DEAN WITTER & CO.
022 B000007 13-2655998
022 C000007 104773
022 D000007 0
022 A000008 MERRILL LYNCH, PIERCE, FENNER & SMITH INC.
022 B000008 13-5674085
022 C000008 30779
022 D000008 33275
022 A000009 BANK OF AMERICA NT & SA
022 B000009 94-1687665
022 C000009 24923
022 D000009 14610
022 A000010 NEWMAN & ASSOCIATES, INC.
022 B000010 84-0775574
022 C000010 18425
022 D000010 17550
023 C000000 1044622
023 D000000 700280
028 A010000 256600
028 A020000 1286
028 A030000 0
028 A040000 254711
028 B010000 191412
028 B020000 1029
028 B030000 0
028 B040000 206268
028 C010000 266150
028 C020000 930
028 C030000 0
<PAGE> PAGE 3
028 C040000 196202
028 D010000 270303
028 D020000 1294
028 D030000 0
028 D040000 221014
028 E010000 337915
028 E020000 1353
028 E030000 0
028 E040000 427015
028 F010000 156796
028 F020000 1638
028 F030000 0
028 F040000 176256
028 G010000 1479176
028 G020000 7530
028 G030000 0
028 G040000 1481466
028 H000000 0
029 000000 N
030 A000000 0
030 B000000 0.00
030 C000000 0.00
031 A000000 0
031 B000000 0
032 000000 0
033 000000 0
034 000000 N
035 000000 0
036 B000000 0
037 000000 N
038 000000 0
039 000000 N
040 000000 Y
041 000000 Y
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 14
044 000000 45
062 A000000 Y
062 B000000 0.0
062 C000000 0.0
062 D000000 0.0
062 E000000 100.2
062 F000000 0.0
062 G000000 0.0
<PAGE> PAGE 4
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 33
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 6
072 B000000 9739
072 C000000 0
072 D000000 0
072 E000000 0
072 F000000 1453
072 G000000 0
072 H000000 0
072 I000000 147
072 J000000 29
072 K000000 0
072 L000000 22
072 M000000 13
072 N000000 13
072 O000000 1
072 P000000 0
072 Q000000 0
072 R000000 13
072 S000000 21
072 T000000 14
072 U000000 0
072 V000000 3
072 W000000 6
072 X000000 1735
072 Y000000 3
072 Z000000 8007
072AA000000 6
<PAGE> PAGE 5
072BB000000 0
072CC010000 4
072CC020000 0
072DD010000 7849
072DD020000 159
072EE000000 0
073 A010000 0.0140
073 A020000 0.0120
073 B000000 0.0000
073 C000000 0.0000
074 A000000 0
074 B000000 0
074 C000000 547797
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 5593
074 M000000 52
074 N000000 553442
074 O000000 0
074 P000000 237
074 Q000000 0
074 R010000 0
074 R020000 0
074 R030000 0
074 R040000 6751
074 S000000 0
074 T000000 546454
074 U010000 537954
074 U020000 8707
074 V010000 1.00
074 V020000 1.00
074 W000000 0.9991
074 X000000 3290
074 Y000000 0
075 A000000 567525
075 B000000 0
076 000000 0.00
077 A000000 Y
077 Q010000 Y
SIGNATURE MICHAEL CONDON
TITLE ASSISTANT TREASURER