<PAGE> PAGE 1
000 B000000 01/31/1999
000 C000000 0000356409
000 D000000 N
000 E000000 NF
000 F000000 Y
000 G000000 N
000 H000000 N
000 I000000 6.1
000 J000000 A
001 A000000 MSDW U.S. GOVERNMENT MONEY MARKET TRUST
001 B000000 811-3326
001 C000000 2123922550
002 A000000 TWO WORLD TRADE CENTER
002 B000000 NEW YORK
002 C000000 NY
002 D010000 10048
003 000000 N
004 000000 N
005 000000 N
006 000000 N
007 A000000 N
007 B000000 0
007 C010100 1
007 C010200 2
007 C010300 3
007 C010400 4
007 C010500 5
007 C010600 6
007 C010700 7
007 C010800 8
007 C010900 9
007 C011000 10
007 C011100 11
007 C011200 12
007 C011300 13
007 C011400 14
007 C011500 15
007 C011600 16
007 C011700 17
007 C011800 18
007 C011900 19
007 C012000 20
007 C012100 21
007 C012200 22
007 C012300 23
007 C012400 24
007 C012500 25
007 C012600 26
007 C012700 27
007 C012800 28
007 C012900 29
<PAGE> PAGE 2
007 C013000 30
007 C013100 31
007 C013200 32
007 C013300 33
007 C013400 34
007 C013500 35
007 C013600 36
007 C013700 37
007 C013800 38
007 C013900 39
007 C014000 40
007 C014100 41
007 C014200 42
007 C014300 43
007 C014400 44
007 C014500 45
007 C014600 46
007 C014700 47
007 C014800 48
007 C014900 49
007 C015000 50
007 C015100 51
007 C015200 52
007 C015300 53
007 C015400 54
007 C015500 55
007 C015600 56
007 C015700 57
007 C015800 58
007 C015900 59
007 C016000 60
007 C016100 61
007 C016200 62
007 C016300 63
007 C016400 64
007 C016500 65
007 C016600 66
007 C016700 67
007 C016800 68
007 C016900 69
007 C017000 70
008 A000001 MORGAN STANLEY DEAN WITTER ADVISORS INC.
008 B000001 A
008 C000001 801-42061
008 D010001 NEW YORK
008 D020001 NY
008 D030001 10048
011 A000001 MORGAN STANLEY DEAN WITTER DISTRIBUTORS INC.
011 B000001 8-45262
011 C010001 NEW YORK
011 C020001 NY
<PAGE> PAGE 3
011 C030001 10048
012 A000001 MORGAN STANLEY DEAN WITTER TRUST FSB.
012 B000001 84-1785
012 C010001 JERSEY CITY
012 C020001 NJ
012 C030001 07311
013 A000001 PRICEWATERHOUSECOOPERS LLP
013 B010001 NEW YORK
013 B020001 NY
013 B030001 10036
014 A000001 DEAN WITTER REYNOLDS INC.
014 B000001 8-14172
014 A000002 MORGAN STANLEY & CO. INCORPORATED
014 B000002 8-15869
015 A000001 THE BANK OF NEW YORK
015 B000001 C
015 C010001 NEW YORK
015 C020001 NY
015 C030001 10286
015 E010001 X
018 000000 Y
019 A000000 Y
019 B000000 120
019 C000000 MSDW-FUNDS
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 WARBURG DILLON READ LLC.
022 B000001 13-3873456
022 C000001 7865000
022 D000001 0
022 A000002 GOLDMAN SACHS AND CO.
022 B000002 13-5108880
022 C000002 793298
022 D000002 0
022 A000003 FIRST CHICAGO CAPITAL MARKETS INC.
022 B000003 36-3595942
022 C000003 654765
022 D000003 0
022 A000004 MERRILL LYNCH, PIERCE, FENNER & SMITH INC.
022 B000004 13-5674085
022 C000004 528728
022 D000004 0
<PAGE> PAGE 4
022 A000005 NATIONSBANC MONTGOMERY SECURITIES LLC
022 B000005 56-2058405
022 C000005 458166
022 D000005 0
022 A000006 LEHMAN BROTHERS INC.
022 B000006 13-2518466
022 C000006 414349
022 D000006 0
022 A000007 BANK OF NEW YORK (THE)
022 B000007 13-5160382
022 C000007 401828
022 D000007 0
022 A000008 BANCAMERICA ROBERTSON STEPHENS
022 B000008 95-4035346
022 C000008 374920
022 D000008 0
022 A000009 CS FIRST BOSTON CORP.
022 B000009 13-5659485
022 C000009 312556
022 D000009 29640
022 A000010 MORGAN (J.P.) SECURITIES INC.
022 B000010 13-3224016
022 C000010 273204
022 D000010 0
023 C000000 12775058
023 D000000 29640
024 000000 Y
025 A000001 BANK OF NEW YORK (THE)
025 B000001 13-5160382
025 C000001 D
025 D000001 2085
025 D000002 0
025 D000003 0
025 D000004 0
025 D000005 0
025 D000006 0
025 D000007 0
025 D000008 0
026 A000000 N
026 B000000 N
026 C000000 N
026 D000000 Y
026 E000000 N
026 F000000 N
026 G010000 N
026 G020000 N
026 H000000 N
027 000000 Y
028 A010000 167858
028 A020000 3205
028 A030000 0
<PAGE> PAGE 5
028 A040000 143276
028 B010000 176098
028 B020000 3744
028 B030000 0
028 B040000 176223
028 C010000 189972
028 C020000 3583
028 C030000 0
028 C040000 145152
028 D010000 160730
028 D020000 3464
028 D030000 0
028 D040000 154036
028 E010000 178209
028 E020000 3821
028 E030000 0
028 E040000 185239
028 F010000 230341
028 F020000 3245
028 F030000 0
028 F040000 204330
028 G010000 1103208
028 G020000 21062
028 G030000 0
028 G040000 1008256
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 904
<PAGE> PAGE 6
044 000000 0
045 000000 Y
046 000000 N
047 000000 Y
048 000000 0.000
048 A010000 500000
048 A020000 0.500
048 B010000 250000
048 B020000 0.425
048 C010000 250000
048 C020000 0.375
048 D010000 500000
048 D020000 0.350
048 E010000 500000
048 E020000 0.325
048 F010000 500000
048 F020000 0.300
048 G010000 500000
048 G020000 0.275
048 H010000 0
048 H020000 0.000
048 I010000 0
048 I020000 0.000
048 J010000 0
048 J020000 0.000
048 K010000 3000000
048 K020000 0.250
049 000000 N
050 000000 N
051 000000 N
052 000000 N
053 A000000 N
054 A000000 Y
054 B000000 Y
054 C000000 Y
054 D000000 N
054 E000000 N
054 F000000 N
054 G000000 Y
054 H000000 Y
054 I000000 N
054 J000000 Y
054 K000000 N
054 L000000 Y
054 M000000 Y
054 N000000 N
054 O000000 N
055 A000000 N
055 B000000 N
056 000000 Y
057 000000 N
<PAGE> PAGE 7
058 A000000 N
059 000000 Y
060 A000000 Y
060 B000000 Y
061 000000 1000
062 A000000 Y
062 B000000 0.7
062 C000000 99.8
062 D000000 0.2
062 E000000 0.0
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 56
063 B000000 0.0
064 A000000 N
064 B000000 N
066 A000000 N
067 000000 N
068 A000000 N
068 B000000 N
069 000000 N
070 A010000 Y
070 A020000 Y
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
070 J010000 N
<PAGE> PAGE 8
070 J020000 N
070 K010000 N
070 K020000 N
070 L010000 N
070 L020000 N
070 M010000 N
070 M020000 N
070 N010000 Y
070 N020000 N
070 O010000 N
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 12
072 B000000 50616
072 C000000 0
072 D000000 0
072 E000000 0
072 F000000 4236
072 G000000 0
072 H000000 0
072 I000000 3029
072 J000000 60
072 K000000 0
072 L000000 214
072 M000000 17
072 N000000 243
072 O000000 0
072 P000000 0
072 Q000000 0
072 R000000 35
072 S000000 17
072 T000000 904
072 U000000 0
072 V000000 0
072 W000000 12
072 X000000 8767
072 Y000000 0
072 Z000000 41849
072AA000000 40
072BB000000 0
072CC010000 0
072CC020000 0
<PAGE> PAGE 9
072DD010000 41850
072DD020000 0
072EE000000 40
073 A010000 0.0453
073 A020000 0.0000
073 B000000 0.0000
073 C000000 0.0000
074 A000000 90
074 B000000 2085
074 C000000 1022232
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 328
074 M000000 36
074 N000000 1024771
074 O000000 0
074 P000000 586
074 Q000000 0
074 R010000 0
074 R020000 0
074 R030000 0
074 R040000 6720
074 S000000 0
074 T000000 1017465
074 U010000 1017463
074 U020000 0
074 V010000 1.00
074 V020000 0.00
074 W000000 1.0003
074 X000000 339011
074 Y000000 0
075 A000000 932777
075 B000000 0
076 000000 0.00
077 A000000 Y
077 B000000 Y
077 C000000 N
077 D000000 N
077 E000000 N
077 F000000 N
077 G000000 N
077 H000000 N
077 I000000 N
077 J000000 N
077 K000000 N
<PAGE> PAGE 10
077 L000000 N
077 M000000 N
077 N000000 N
077 O000000 N
077 P000000 Y
077 Q010000 N
077 Q020000 N
077 Q030000 N
078 000000 N
080 A000000 ICI MUTUAL INSURANCE COMPANY
080 B000000 GULF CHUBB VIGILANT RELIANCE
080 C000000 110000
081 A000000 Y
081 B000000 119
082 A000000 N
082 B000000 0
083 A000000 N
083 B000000 0
084 A000000 N
084 B000000 0
085 A000000 Y
085 B000000 N
086 A010000 0
086 A020000 0
086 B010000 0
086 B020000 0
086 C010000 0
086 C020000 0
086 D010000 0
086 D020000 0
086 E010000 0
086 E020000 0
086 F010000 0
086 F020000 0
SIGNATURE BARRY FINK
TITLE VICE PRESIDENT
<TABLE> <S> <C>
<ARTICLE> 6
<LEGEND>
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
ANNUAL FDS
1-31-1999
</LEGEND>
<CIK> 0000356409
<NAME> MSDW U.S. GOVERNMENT MONEY MARKET TRUST
<S> <C>
<PERIOD-TYPE> 6-MOS
<FISCAL-YEAR-END> JAN-31-1999
<PERIOD-END> JAN-31-1999
<INVESTMENTS-AT-COST> 1,024,316,284
<INVESTMENTS-AT-VALUE> 1,024,316,284
<RECEIVABLES> 328,520
<ASSETS-OTHER> 126,227
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 1,024,771,031
<PAYABLE-FOR-SECURITIES> (6,555,859)
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> (750,409)
<TOTAL-LIABILITIES> (7,306,268)
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 1,017,463,124
<SHARES-COMMON-STOCK> 1,017,463,124
<SHARES-COMMON-PRIOR> 890,569,126
<ACCUMULATED-NII-CURRENT> 1,639
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> 0
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 0
<NET-ASSETS> 1,017,464,763
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 50,615,622
<OTHER-INCOME> 0
<EXPENSES-NET> (8,766,643)
<NET-INVESTMENT-INCOME> 41,848,979
<REALIZED-GAINS-CURRENT> 40,360
<APPREC-INCREASE-CURRENT> 0
<NET-CHANGE-FROM-OPS> 41,889,339
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (41,849,500)
<DISTRIBUTIONS-OF-GAINS> (40,360)
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 2,239,344,299
<NUMBER-OF-SHARES-REDEEMED> (2,155,004,652)
<SHARES-REINVESTED> 41,717,140
<NET-CHANGE-IN-ASSETS> 126,893,477
<ACCUMULATED-NII-PRIOR> 2,160
<ACCUMULATED-GAINS-PRIOR> 0
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> (4,236,205)
<GROSS-ADVISORY-FEES> 0
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> (8,766,643)
<AVERAGE-NET-ASSETS> 932,777,233
<PER-SHARE-NAV-BEGIN> 1.0
<PER-SHARE-NII> 0.045
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> (0.045)
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 1.00
<EXPENSE-RATIO> 0.94
<AVG-DEBT-OUTSTANDING> 0
<AVG-DEBT-PER-SHARE> 0
</TABLE>
