PAGE  1
000 B000000 12/31/2009
000 C000000 0001385763
000 D000000 N
000 E000000 NF
000 F000000 Y
000 G000000 N
000 H000000 N
000 I000000 6.1
000 J000000 A
001 A000000 NUVEEN CORE EQUITY ALPHA FUND
001 B000000 811-220003
001 C000000 3129178200
002 A000000 333 WEST WACKER DRIVE
002 B000000 CHICAGO
002 C000000 IL
002 D010000 60606
002 D020000 1286
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
008 A000001 NUVEEN ASSET MANAGEMENT
008 B000001 A
008 C000001 801-14147
008 D010001 CHICAGO
008 D020001 IL
008 D030001 60606
008 D040001 1286
008 A000002 ENHANCED INVESTMENT TECHNOLOGIES (INTECH)
008 B000002 A
008 C000002 801-60987
008 D010002 PALM BEACH GARDENS
008 D020002 FL
008 D030002 33410
012 A000001 EQUISERVE INC.
012 B000001 84-05925
012 C010001 PROVIDENCE
012 C020001 RI
012 C030001 02940
      PAGE  2
013 A000001 PRICEWATERHOUSECOOPERS LLP
013 B010001 CHICAGO
013 B020001 IL
013 B030001 60606
014 A000001 NUVEEN INVESTMENTS, LLC
014 B000001 8-13464
015 A000001 STATE STREET BANK AND TRUST COMPANY
015 B000001 C
015 C010001 BOSTON
015 C020001 MA
015 C030001 02110
015 E010001 X
018  000000 Y
019 A000000 Y
019 B000000  199
019 C000000 NUVEENFUND
020 A000001 DEUTSCHE BANK SECURITIES INC
020 B000001 13-2730828
020 C000001     23
020 A000002 CREDIT SUISSE
020 B000002 13-5659485
020 C000002     19
020 A000003 WEEDEN & CO
020 B000003 13-3364318
020 C000003     19
020 A000004 MERRILL LYNCH, PIERCE, FENNER & SMITH, INC
020 B000004 13-5674085
020 C000004     19
020 A000005 GOLDMAN SACHS & CO
020 B000005 13-5108880
020 C000005     18
020 A000006 ROSENBLATT SECURITIES
020 B000006 13-2975865
020 C000006     17
020 A000007 BNY BROKERAGE
020 B000007 13-3989198
020 C000007     17
020 A000008 CAPITAL INSTITUTIONAL
020 B000008 75-1565705
020 C000008     15
020 A000009 GUZMAN & CO
020 B000009 59-2764363
020 C000009     13
020 A000010 INSTINET
020 B000010 13-3443395
020 C000010     13
021  000000      189
022 A000001 MERRILL LYNCH
022 B000001 13-5674085
022 C000001     31046
022 D000001     36378
      PAGE  3
022 A000002 DEUTSCHE BANK
022 B000002 13-2730828
022 C000002     24183
022 D000002     21942
022 A000003 LYNCH, JONES & RYAN
022 B000003 13-3356934
022 C000003     18944
022 D000003     24699
022 A000004 CREDIT SUISSE
022 B000004 13-5659485
022 C000004     16886
022 D000004     21451
022 A000005 WEEDEN & CO
022 B000005 13-3364318
022 C000005     17103
022 D000005     20501
022 A000006 GOLDMAN SACHS
022 B000006 13-5108880
022 C000006     17069
022 D000006     18743
022 A000007 ROSENBLATT SECURITIES
022 B000007 13-2975865
022 C000007     17526
022 D000007     16837
022 A000008 CAPITAL INSITUTIONAL
022 B000008 75-1565705
022 C000008     16093
022 D000008     13955
022 A000009 INSTINET CORP
022 B000009 13-3443395
022 C000009     15449
022 D000009     13927
022 A000010 GUZMAN & CO
022 B000010 59-2764363
022 C000010     12680
022 D000010     13149
023 C000000     208171
023 D000000     224672
024  000000 N
025 D000001       0
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
      PAGE  4
026 E000000 N
026 F000000 N
026 G010000 N
026 G020000 N
026 H000000 N
027  000000 N
028 A010000         0
028 A020000         0
028 A030000         0
028 A040000         0
028 B010000         0
028 B020000         0
028 B030000         0
028 B040000         0
028 C010000         0
028 C020000         0
028 C030000         0
028 C040000         0
028 D010000         0
028 D020000         0
028 D030000         0
028 D040000         0
028 E010000         0
028 E020000         0
028 E030000         0
028 E040000         0
028 F010000         0
028 F020000         0
028 F030000         0
028 F040000         0
028 G010000         0
028 G020000         0
028 G030000         0
028 G040000         0
028 H000000         0
030 A000000      0
030 B000000  0.00
030 C000000  0.00
031 A000000      0
031 B000000      0
032  000000      0
033  000000      0
035  000000      0
036 B000000      0
038  000000      0
042 A000000   0
042 B000000   0
042 C000000   0
042 D000000   0
042 E000000   0
042 F000000   0
      PAGE  5
042 G000000   0
042 H000000   0
043  000000      0
044  000000      0
045  000000 Y
046  000000 N
047  000000 N
048  000000  0.000
048 A010000        0
048 A020000 0.000
048 B010000        0
048 B020000 0.000
048 C010000        0
048 C020000 0.000
048 D010000        0
048 D020000 0.000
048 E010000        0
048 E020000 0.000
048 F010000        0
048 F020000 0.000
048 G010000        0
048 G020000 0.000
048 H010000        0
048 H020000 0.000
048 I010000        0
048 I020000 0.000
048 J010000        0
048 J020000 0.000
048 K010000        0
048 K020000 0.000
049  000000 N
050  000000 N
051  000000 N
052  000000 Y
053 A000000 N
054 A000000 Y
054 B000000 N
054 C000000 N
054 D000000 N
054 E000000 N
054 F000000 N
054 G000000 N
054 H000000 Y
054 I000000 N
054 J000000 Y
054 K000000 N
054 L000000 N
054 M000000 Y
054 N000000 N
054 O000000 Y
055 A000000 Y
      PAGE  6
055 B000000 N
056  000000 Y
057  000000 N
058 A000000 N
059  000000 Y
060 A000000 Y
060 B000000 Y
061  000000        0
062 A000000 N
062 B000000   0.0
062 C000000   0.0
062 D000000   0.0
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   0
063 B000000  0.0
066 A000000 Y
066 B000000 N
066 C000000 N
066 D000000 N
066 E000000 N
066 F000000 N
066 G000000 Y
067  000000 N
068 A000000 N
068 B000000 N
069  000000 N
070 A010000 Y
070 A020000 Y
070 B010000 Y
070 B020000 Y
070 C010000 Y
070 C020000 N
070 D010000 N
070 D020000 N
070 E010000 Y
070 E020000 N
070 F010000 Y
070 F020000 Y
      PAGE  7
070 G010000 Y
070 G020000 N
070 H010000 Y
070 H020000 N
070 I010000 Y
070 I020000 N
070 J010000 Y
070 J020000 N
070 K010000 Y
070 K020000 N
070 L010000 Y
070 L020000 N
070 M010000 Y
070 M020000 N
070 N010000 Y
070 N020000 N
070 O010000 Y
070 O020000 N
070 P010000 N
070 P020000 N
070 Q010000 N
070 Q020000 N
070 R010000 Y
070 R020000 N
071 A000000    208219
071 B000000    224742
071 C000000    185807
071 D000000  112
072 A000000 12
072 B000000       17
072 C000000     4447
072 D000000        0
072 E000000        0
072 F000000     1794
072 G000000        0
072 H000000        0
072 I000000        0
072 J000000      196
072 K000000       24
072 L000000       47
072 M000000        6
072 N000000        0
072 O000000        0
072 P000000        0
072 Q000000        0
072 R000000       22
072 S000000       -2
072 T000000        0
072 U000000        0
072 V000000        0
072 W000000       98
      PAGE  8
072 X000000     2185
072 Y000000        0
072 Z000000     2279
072AA000000        0
072BB000000    29804
072CC010000    68135
072CC020000        0
072DD010000        0
072DD020000        0
072EE000000        0
073 A010000   0.1500
073 A020000   0.0000
073 B000000   0.0000
073 C000000   0.9500
074 A000000        0
074 B000000     4196
074 C000000     5000
074 D000000        0
074 E000000        0
074 F000000   203057
074 G000000        0
074 H000000        0
074 I000000        0
074 J000000     6291
074 K000000        0
074 L000000      251
074 M000000        7
074 N000000   218802
074 O000000     6254
074 P000000      169
074 Q000000        0
074 R010000        0
074 R020000        0
074 R030000      763
074 R040000      249
074 S000000        0
074 T000000   211367
074 U010000    16034
074 U020000        0
074 V010000    13.18
074 V020000     0.00
074 W000000   0.0000
074 X000000        6
074 Y000000     6942
075 A000000        0
075 B000000   189847
076  000000    12.21
077 A000000 Y
077 B000000 Y
077 Q020000 Y
078  000000 N
      PAGE  9
080 A000000 CHUBB GROUP OF INSURANCE COMPANIES
080 B000000 BERKLEY, GREAT AMERICAN, ST. PAUL & CNA
080 C000000   110000
081 A000000 Y
081 B000000 198
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    255
086 B020000   2630
086 C010000      0
086 C020000      0
086 D010000      0
086 D020000      0
086 E010000      0
086 E020000      0
086 F010000      0
086 F020000      0
087 A010000 COMMON STOCK
087 A020000 67090X107
087 A030000 JCE
088 A000000 N
088 B000000 N
088 C000000 N
088 D000000 N
SIGNATURE   STEPHEN D. FOY
TITLE       V.P. & CONTROLLER