UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-CSR

              CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT
                              INVESTMENT COMPANIES

                  Investment Company Act File Number: 811-8059

                    Cohen & Steers Special Equity Fund, Inc.
               (Exact name of registrant as specified in charter)

                      757 Third Avenue, New York, NY 10017
               (Address of principal executive offices) (Zip code)

                                Robert H. Steers
                     Cohen & Steers Capital Management, Inc.
                                757 Third Avenue
                            New York, New York 10017
                     (Name and address of agent for service)

       Registrant's telephone number, including area code: (212) 832-3232

                      Date of fiscal year end: December 31

                     Date of reporting period: June 30, 2004








Item 1. Reports to Stockholders.

The registrant's semi-annual report to shareholders, for the period ended June
30, 2004 is included herein.

Item 2. Code of Ethics.

Not applicable.

Item 3. Audit Committee Financial Expert.

Not applicable.

Item 4. Principal Accountant Fees and Services.

Not applicable.

Item 5. Audit Committee of Listed Registrants.

Not applicable.

Item 6. Schedule of Investments.

Not applicable.

Item 7. Disclosure of Proxy Voting Policies and Procedures for Closed-End
Management Investment Companies.

Not applicable.

Item 8. Purchases of Equity Securities by Closed-End Management Investment
Company and Affiliated Purchasers.

Not applicable.

Item 9. Submission of Matters to a Vote of Security Holders.

Not applicable.

Item 10. Controls and Procedures.

(a) The registrant's principal executive officer and principal financial officer
have concluded that the registrant's disclosure controls and procedures are
sufficient to ensure that information required to be disclosed by the registrant
in this Form N-CSR was recorded, processed, summarized and reported within the
time periods specified in the Securities and Exchange








Commission's rules and forms, based upon such officers' evaluation of these
controls and procedures as of a date within 90 days of the filing date of this
report.

(b) There were no changes in the registrant's internal control over financial
reporting that occurred during the registrant's most recent fiscal half-year
(the registrant's second fiscal half-year in the case of an annual report) that
has materially affected, or is reasonably likely to materially affect, the
registrant's internal control over financial reporting.

Item 11. Exhibits.

(a) (2) Certifications of principal executive officer and principal financial
officer as required by Rule 30a-2(a) under the Investment Company Act of 1940.

(b) Certifications of chief executive officer and chief financial officer as
required by Rule 30a-2(b) under the Investment Company Act of 1940.









                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

COHEN & STEERS SPECIAL EQUITY FUND, INC.

     By: /s/ Robert H. Steers
         -------------------------------
             Name: Robert H. Steers
             Title: Chairman

         Date: August 19, 2004

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.


    By: /s/ Robert H. Steers                 By: /s/ Martin Cohen
        -------------------------------          -----------------------------
            Name: Robert H. Steers                   Name: Martin Cohen
            Title: Chairman, Secretary               Title: President, Treasurer
                    and principal executive                  and principal
                    officer                                  financial officer

     Date: August 19, 2004








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

July 26, 2004

To Our Shareholders:

    We are pleased to submit to you our report for the quarter and six months
ended June 30, 2004. The net asset value on that date was $42.23 per share. A
semiannual dividend of $0.55 per share was declared for shareholders of record
on June 17, 2004 and was paid on June 18, 2004.

INVESTMENT REVIEW

    For the quarter, Cohen & Steers Special Equity Fund had a total return,
based on income and change in net asset value, of  -1.3%. This compares to the
NAREIT Equity REIT Index's(a) total return of  -5.8% and the S&P 500 Index's
total return of 1.5%. For the six months ended June 30, 2004, Cohen & Steers
Special Equity Fund had a total return of 11.0% versus the NAREIT Equity REIT
Index's total return of 5.5% and the S&P 500 Index's Total Return of 3.3%.

    The second quarter of 2004 brought further evidence of a strengthening U.S.
economic recovery. The release of the March increase in the U.S. non-farm
payrolls report in early April forced many of the pessimistic economic naysayers
to acknowledge that the recovery was, in fact, for real.

    The second quarter began with a dramatic decline in REIT stock prices,
followed by a dramatic rebound and, most importantly, in our view a decisive
rotation in leadership within the REIT market. By way of review, the March jobs
report took the capital markets by surprise on April 2 and sent the bond market
reeling, resulting in the worst quarter for the bond market since the first
quarter of 1994. REITs dropped 18% from their highs at the end of March, before
bottoming on May 10. We characterized this decline as technical in nature,
driven by the valuation concerns of some investors, and one that we believed
presented an attractive investment opportunity. In our view, the very jobs
report that set off the decline in REIT share prices was likely to contribute to
improving real estate fundamentals and greater cash flow for REITs.

    We are pleased to report that since then REITs have rebounded significantly,
recording a 14% total return from May 10 through the end of June, and were one
of the best performing asset classes over this time period. The strong returns
of the last two months are certainly inconsistent with the notion put forward by
some pundits that REITs tipped into a bear market in the second quarter in
sympathy with the bond market. In fact, if the first half of 2004 is a proper
guide, we believe REITs are on pace to deliver the low- to mid-teens total
return profile that is consistent with the sector's long-term average.

    While many observers focused on this uncharacteristic volatility in REIT
stock prices, the more interesting story in the second quarter was a powerful
rotation of leadership within the REIT market. The defensive and

- -------------------
(a) The NAREIT Equity REIT Index is an unmanaged, market capitalization weighted
    index of all publicly traded REITs that invest predominantly in the equity
    ownership of real estate. The index is designed to reflect the performance
    of all publicly traded equity REITs as a whole.

- --------------------------------------------------------------------------------
                                       1








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

higher-yielding issues, that led the REIT group since 2001, ceded their market
leadership to the more cyclically inclined companies that we believe will
respond to the economic recovery most quickly and most dramatically. If this
trend continues, as we believe it will, it will provide further evidence that
investors are looking at REITs again not just for their dividend yield, but also
for their total return potential. Our quantitative analysis of second quarter
trends found a very strong relationship between the prospects for growth in REIT
operating income growth at the property level (the primary indicator of real
estate fundamentals) and its total return. Conversely, our analysis of the
second quarter showed a very strong opposite correlation between current
dividend yield and second quarter total return. It has almost universally been
the case that REITs with the least favorable growth prospects require a higher
current yield to compensate investors for lower future cash flow growth.

    It is not surprising that the fund's portfolio did well in this second
quarter environment since our investment process emphasizes selecting stocks
that we view as offering attractive future cash flow growth prospects and strong
potential for rising real estate asset values. We positioned our portfolio some
time ago to capitalize on this expected rotation, believing that the U.S.
economy was on the verge of a sustainable and powerful economic recovery. In our
view, this secular shift would create significant job growth, higher building
occupancies and rents, and significantly higher cash flow for REITs.
Accordingly, we overweighted the most cyclical property sectors, the apartment
and hotel sectors, for example, which led the way in the second quarter,
returning 2.1% and 3.7%, respectively. These property types are characterized by
short leases (approximately one year and one day, respectively) and more
variable demand patterns which enable the landlord to raise occupancies and
rents very quickly in an economic upturn.

    Conversely, we underweighted more defensive and interest-rate-sensitive
sectors such as the health care and shopping center sectors, which
underperformed the overall REIT market, declining 13.4% and 7.5%, respectively.
These property types are characterized by very long lease terms and relatively
consistent demand profiles and as a result do not respond proportionately to
accelerating economic growth. The regional mall sector, which also had been a
leader for several quarters, became a laggard in the second quarter, declining
11.5%. The mall sector normally exhibits some cyclical characteristics, but in
addition has benefited from a secular consolidation of ownership, which has
driven this cyclical group throughout the economic downturn.

    As a result of both our stock selection and property sector weights, the
fund significantly outperformed its benchmark in the second quarter. Our stock
selection in the apartment, office, hotel and regional mall sectors were the
largest drivers of our portfolio outperformance as we sought out the geographic
areas and companies that we believe would best respond to the resurgent demand
for real estate. Our overweights in the apartment and hotel sectors were also
major contributors. Several months ago our fundamental research pointed to a
view that greater job growth and higher interest rates were going to stimulate a
significant rebound in demand for apartments, and our valuation model thus
indicated that we should take our apartment position from a significant
underweight to an overweight. In the first quarter, REIT investors came to
appreciate this view more broadly and as a result the apartment sector was one
of the best performing sectors in the second quarter. Finally, our underweight
in the health care sector was also a significant contributor to performance.
There were no significant detractors from our relative performance during the
quarter.

- --------------------------------------------------------------------------------
                                       2








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

    Punctuating what we view is a trend toward a new emphasis on growth for REIT
investors, Simon Property Group, the largest owner of regional malls in the
United States, announced it would acquire Chelsea Property Group. This outlet
center company has consistently had one of the highest cash flow growth rates in
our investment universe. The $5 billion deal is notable because Simon is paying
$66 per share, a 13% premium to Chelsea's pre-announcement price, which already
reflected a 25% premium to Wall Street's consensus opinion of the private market
value of Chelsea's assets. Because Chelsea has such unique growth prospects
Simon is willing to pay a very large premium to the generally recognized value
of the underlying assets and, in our opinion, can still generate a significant
beneficial impact to its own growth rate. Chelsea is a great example of a real
estate company that we believe is truly worth more than just the value of its
bricks and mortar. We would not be surprised if there was more acquisition
activity involving high growth companies.

INVESTMENT OUTLOOK

    In the wake of the REIT stock price decline in the second quarter, many
investors have asked us whether REITs can continue to perform well in what many
are concerned (overly so, in our view) may be a period of rising interest rates.

    Our view has always been and continues to be that real estate fundamentals
are the primary driver of REIT returns over the long run. Still, we regularly
examine the extent to which REITs are correlated with other asset classes. We
have found that over the long term REIT share price behavior has not been
statistically related in any material way to those of bonds or interest rates.
In other words, over time, the performance of the bond market has explained
virtually none of the performance of REITs.

    Over the short term, REITs may appear to correlate with interest rates, as
we have seen recently. However, although we can say with certainty that rising
rates result in poor returns for bonds, the REIT return equation cannot be
solved using interest rates as the only input variable. Importantly, we have
also found that in the 12 months following periods of rising interest rates, as
the dampening effect of higher interest rates on security returns has subsided
and the acceleration of real estate fundamentals has kicked in, REIT performance
historically has been consistently very strong.

    Nonetheless, we cannot ignore the fact that interest rates can have an
impact on REIT earnings and asset values. Higher interest rates will increase
the cost of REITs' debt capital over time, although the impact will be mitigated
by REITs' use of primarily long-term, fixed-rate debt. Higher interest rates may
also result in higher real estate capitalization rates, which would tend to
lower estimates of property values.

    Higher interest rates can also have some beneficial effects on REITs. The
higher inflationary expectations, which are partially driving higher interest
rates, push up the price of building costs, especially inputs like steel,
concrete, lumber, labor and construction period interest. Thus the overall
replacement cost of real estate escalates, which flows through eventually in the
form of higher market rents. Already we are hearing reports that construction
costs have risen by as much as 25% over the past two years. If capitalization
rates were to rise, the return on assets that REITs could achieve on external
acquisitions of property should increase. Furthermore,

- --------------------------------------------------------------------------------
                                       3








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

higher debt costs will tend to choke off development of new, competitive real
estate. These higher debt costs tend to have a greater impact on the private
developers who typically build the majority of new buildings and use a higher
proportion of debt in their capital structure.

    Our conclusion is that, although changes in interest rates have a varied
impact on REITs, the positive and negative impacts have historically tended to
offset one another, such that the overall impact on REIT returns has not
generally been material, thus, the historical lack of correlation. What remains
material is the supply and demand for real estate and how that impacts building
occupancies and rents. The most important thing to recognize in our view about
the prospects for REIT returns is that the job growth that occurred in March of
this year was followed up with continued strong job growth reports for both
April and May, establishing that the economic recovery in the United States is
strong and sustainable and not lacking in any way. With this key economic driver
in place, we believe the prospects for higher building occupancies and rents,
and thus for higher cash flows for REITs, are excellent.

    At this point, with the first dose of Fed tightening already under our belts
and a further rise in interest rates widely anticipated among economists and
investors alike, it is safe to say that whatever impact investors believe rising
interest rates may have on REITs has been well digested by the stock market, the
net effect having been to bring REIT valuations in line with historical norms.
In our view, the favorable prospects for accelerating cash flow growth over the
next couple of years in combination with these valuations give us confidence
that REITs can continue to generate attractive total returns.

Sincerely,

             MARTIN COHEN                ROBET H. STEERS
             MARTIN COHEN                ROBERT H. STEERS
             President                   Chairman

             JOSEPH M. HARVEY            JAMES S. CORL
             JOSEPH M. HARVEY            JAMES S. CORL
             Portfolio Manager           Portfolio Manager


- --------------------------------------------------------------------------------
                                       4








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

           Cohen & Steers is online at cohenandsteers.com

    We have enhanced both the look and features of our Web site
    to give you more information about our company, our funds
    and the REIT market in general.

    ONLINE ACCESS is available for shareholders of Cohen &
    Steers funds whose accounts are held directly with Boston
    Financial Data Services, the fund's transfer agent. After
    registering, you will be able to manage your entire account
    online including purchasing or redeeming shares, updating
    account information, and checking your portfolio holdings.

    Check out our interactive Asset Allocation Tool, which
    allows you to hypothetically add REITs to any portfolio to
    see how they impact expected total returns and risk. Or try
    the Fund Performance Calculator and see how our funds have
    performed versus the S&P 500 Index or Nasdaq composite. As
    always, you can also get daily net asset values, fund fact
    sheets, portfolio highlights, recent news articles and our
    overall insights on the REIT market.

              So visit us today at cohenandsteers.com

- --------------------------------------------------------------------------------
                                       5









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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                            SCHEDULE OF INVESTMENTS
                           JUNE 30, 2004 (UNAUDITED)

<Table>
<Caption>
                                                              NUMBER        VALUE
                                                             OF SHARES    (NOTE 1)
                                                             ---------   -----------
                                                                   
EQUITIES                                            95.93%(a)
    DIVERSIFIED                                      6.82%
         Alexander's(b)....................................      6,800   $ 1,140,632
         Vornado Realty Trust..............................     19,900     1,136,489
                                                                         -----------
                                                                           2,277,121
                                                                         -----------
    HOTEL                                           10.50%
         Hilton Hotels Corp................................     39,400       735,204
         Host Marriott Corp.(b)............................    103,500     1,279,260
         MeriStar Hospitality Corp.(b).....................     47,800       326,952
         Starwood Hotels & Resorts Worldwide...............     26,000     1,166,100
                                                                         -----------
                                                                           3,507,516
                                                                         -----------
    INDUSTRIAL                                       3.79%
         ProLogis..........................................     38,400     1,264,128
                                                                         -----------
    OFFICE                                          16.24%
         Boston Properties.................................     22,700     1,136,816
         CarrAmerica Realty Corp...........................     33,000       997,590
         Highwoods Properties..............................      2,800        65,800
         Mack-Cali Realty Corp.............................     20,800       860,704
         Maguire Properties................................     48,200     1,193,914
         SL Green Realty Corp..............................     25,000     1,170,000
                                                                         -----------
                                                                           5,424,824
                                                                         -----------
    RESIDENTIAL                                     21.28%
       APARTMENT                                    13.62%
         Archstone-Smith Trust.............................     21,800       639,394
         AvalonBay Communities.............................     11,400       644,328
         BRE Properties....................................     27,100       941,725
         Essex Property Trust..............................     11,900       813,365
         Post Properties...................................     23,300       679,195
         Summit Properties.................................     32,400       830,736
                                                                         -----------
                                                                           4,548,743
                                                                         -----------
</Table>

- -------------------
(a) Percentages indicated are based on the net assets of the fund.
(b) Nonincome producing security.

                See accompanying notes to financial statements.
- --------------------------------------------------------------------------------
                                       6








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                     SCHEDULE OF INVESTMENTS -- (CONTINUED)
                           JUNE 30, 2004 (UNAUDITED)

<Table>
<Caption>
                                                              NUMBER        VALUE
                                                             OF SHARES    (NOTE 1)
                                                             ---------   -----------
                                                                   
       MANUFACTURED HOME                             7.66%
         Affordable Residential Communities................     55,000   $   913,000
         Sun Communities...................................     43,700     1,645,305
                                                                         -----------
                                                                           2,558,305
                                                                         -----------
         TOTAL RESIDENTIAL.................................                7,107,048
                                                                         -----------
    SELF STORAGE                                     7.33%
         Public Storage....................................     17,300       795,973
         Shurgard Storage Centers..........................     44,200     1,653,080
                                                                         -----------
                                                                           2,449,053
                                                                         -----------
    SHOPPING CENTER                                 29.97%
       COMMUNITY CENTER                              9.23%
         Developers Diversified Realty Corp................     37,300     1,319,301
         Federal Realty Investment Trust...................     18,200       756,938
         Inland Real Estate Corp...........................     77,300     1,005,673
                                                                         -----------
                                                                           3,081,912
                                                                         -----------
       REGIONAL MALL                                20.74%
         CBL & Associates Properties.......................     18,500     1,017,500
         Macerich Company..................................     14,400       689,328
         Mills Corp........................................     42,000     1,961,400
         Rouse Co..........................................     28,800     1,368,000
         Simon Property Group..............................     12,400       637,608
         Taubman Centers...................................     54,800     1,254,372
                                                                         -----------
                                                                           6,928,208
                                                                         -----------
         TOTAL SHOPPING CENTER.............................               10,010,120
                                                                         -----------
              TOTAL EQUITIES (Identified
                cost -- $27,570,355).......................               32,039,810
                                                                         -----------
</Table>

                See accompanying notes to financial statements.
- --------------------------------------------------------------------------------
                                       7








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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                     SCHEDULE OF INVESTMENTS -- (CONTINUED)
                           JUNE 30, 2004 (UNAUDITED)

<Table>
<Caption>
                                                                PRINCIPAL       VALUE
                                                                  AMOUNT      (NOTE 1)
                                                                ----------   -----------
                                                                    
COMMERCIAL PAPER                                        3.33%
         State Street Corp, 1.10%, due 07/01/2004
            (Identified cost -- $1,113,000)..................   $1,113,000   $ 1,113,000
                                                                ----------   -----------
TOTAL INVESTMENTS (Identified cost -- $28,683,355)     99.26%                 33,152,810
OTHER ASSETS IN EXCESS OF LIABILIITIES............      0.74%                    247,717
                                                                             -----------
NET ASSETS (Equivalent to $42.23 per share based
  on 790,950 shares of capital stock
  outstanding)....................................    100.00%                $33,400,527
                                                      ------                 -----------
                                                      ------                 -----------
</Table>

                See accompanying notes to financial statements.
- --------------------------------------------------------------------------------
                                       8









- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                      STATEMENT OF ASSETS AND LIABILITIES
                           JUNE 30, 2004 (UNAUDITED)

<Table>
                                                           
ASSETS:
    Investments in securities, at value (Identified
       cost -- $28,683,355) (Note 1)........................  $ 33,152,810
    Cash....................................................           648
    Receivable for investment securities sold...............       645,190
    Dividends receivable....................................       150,289
    Receivable for fund shares sold.........................       145,979
    Other assets............................................        25,368
                                                              ------------
         Total Assets.......................................    34,120,284
                                                              ------------
LIABILITIES:
    Payable for investment securities purchased.............       643,106
    Payable to investment advisor...........................        23,578
    Payable for fund shares redeemed........................        21,817
    Payable for professional fees...........................        18,571
    Payable for reports to shareholders.....................         6,963
    Payable to administrator................................           547
    Other liabilities.......................................         5,175
                                                              ------------
         Total Liabilities..................................       719,757
                                                              ------------
NET ASSETS applicable to 790,950 shares of $0.001 par value
  common stock outstanding (Note 5).........................  $ 33,400,527
                                                              ------------
                                                              ------------
NET ASSET VALUE PER SHARE:
  ($33,400,527[div]790,950 shares outstanding)..............  $      42.23
                                                              ------------
                                                              ------------
NET ASSETS consist of:
    Paid-in capital (Notes 1 and 5).........................  $ 48,794,424
    Distributions in excess of net investment income........      (130,978)
    Accumulated net realized loss on investments............   (19,732,374)
    Net unrealized appreciation on investments..............     4,469,455
                                                              ------------
                                                              $ 33,400,527
                                                              ------------
                                                              ------------
</Table>

                See accompanying notes to financial statements.
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                                       9








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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                            STATEMENT OF OPERATIONS
               FOR THE SIX MONTHS ENDED JUNE 30, 2004 (UNAUDITED)

<Table>
                                                           
Investment Income (Note 1):
    Dividend income (net of $702 of foreign withholding
       tax).................................................  $  521,853
    Interest income.........................................       2,052
                                                              ----------
         Total Income.......................................     523,905
                                                              ----------
Expenses:
    Investment advisory fees (Note 2).......................     141,220
    Reports to shareholders.................................      42,653
    Professional fees.......................................      35,358
    Directors' fees and expenses (Note 2)...................      18,706
    Registration and filing fees............................      13,245
    Custodian fees and expenses.............................       9,790
    Transfer agent fees.....................................       7,626
    Administration fees (Note 2)............................       5,330
    Line of credit fees and expenses (Note 6)...............         793
    Miscellaneous...........................................       7,535
                                                              ----------
         Total Expenses.....................................     282,256
    Reduction of Expenses (Note 2)..........................     (46,890)
                                                              ----------
         Net Expenses.......................................     235,366
                                                              ----------
Net Investment Income.......................................     288,539
                                                              ----------

Net Realized and Unrealized Gain/(Loss) on Investments:
    Net realized gain on investments........................   2,981,580
    Net change in unrealized depreciation on investments....    (174,412)
                                                              ----------
         Net realized and unrealized gain/(loss) on
            investments.....................................   2,807,168
                                                              ----------
Net Increase in Net Assets Resulting from Operations........  $3,095,707
                                                              ----------
                                                              ----------
</Table>

                See accompanying notes to financial statements.
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                                       10








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                 STATEMENT OF CHANGES IN NET ASSETS (UNAUDITED)

<Table>
<Caption>
                                                        FOR THE             FOR THE
                                                    SIX MONTHS ENDED      YEAR ENDED
                                                     JUNE 30, 2004     DECEMBER 31, 2003
                                                     -------------     -----------------
                                                                 
Change in Net Assets:
    From Operations:
         Net investment income....................    $   288,539         $   384,184
         Net realized gain on investments.........      2,981,580           4,148,622
         Net change in unrealized
            appreciation/(depreciation) on
            investments...........................       (174,412)          3,710,763
                                                      -----------         -----------
              Net increase in net assets resulting
                from operations...................      3,095,707           8,243,569
                                                      -----------         -----------
    Dividends and Distributions to Shareholders
       from (Note 1):
         Net investment income....................       (419,517)         (1,143,611)
                                                      -----------         -----------
    Capital Stock Transactions (Note 5):
         Increase in net assets from fund share
            transactions..........................      2,249,530           3,169,414
                                                      -----------         -----------
              Total increase in net assets........      4,925,720          10,269,372
    Net Assets
         Beginning of period......................     28,474,807          18,205,435
                                                      -----------         -----------
         End of period(a).........................    $33,400,527         $28,474,807
                                                      -----------         -----------
                                                      -----------         -----------
</Table>

- -------------------

(a) Includes distributions in excess of net investment income of $130,978 and
    $0 at June 30, 2004 and December 31, 2003, respectively.

                See accompanying notes to financial statements.
- --------------------------------------------------------------------------------
                                       11









- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                        FINANCIAL HIGHLIGHTS (UNAUDITED)

    The following table includes selected data for a share outstanding
throughout each period and other performance information derived from the
financial statements. It should be read in conjunction with the financial
statements and notes thereto.

<Table>
<Caption>
                                                          FOR THE SIX          FOR THE YEAR ENDED DECEMBER 31,
                                                         MONTHS ENDED     ------------------------------------------
PER SHARE OPERATING PERFORMANCE:                         JUNE 30, 2004     2003     2002     2001     2000     1999
- --------------------------------                        ---------------   ------   ------   ------   ------   ------
                                                                                            
Net asset value, beginning of period..................       $38.55       $27.50   $26.63   $26.60   $26.76   $20.88
                                                             ------       ------   ------   ------   ------   ------
Income from investment operations:
   Net investment income..............................         0.37(a)      0.64     0.73     0.69     0.85     0.07
   Net realized and unrealized gain/(loss) on
     investments......................................         3.81        12.06     1.29     0.49     0.01     5.92
                                                             ------       ------   ------   ------   ------   ------
       Total income from investment operations........         4.18        12.70     2.02     1.18     0.86     5.99
                                                             ------       ------   ------   ------   ------   ------
Less dividends and distributions to shareholders from:
   Net investment income..............................        (0.55)       (1.67)   (1.21)   (0.52)   (1.02)   (0.07)
   Tax return of capital..............................           --           --       --    (0.63)      --    (0.04)
                                                             ------       ------   ------   ------   ------   ------
       Total dividends and distributions to
         shareholders.................................        (0.55)       (1.67)   (1.21)   (1.15)   (1.02)   (0.11)
                                                             ------       ------   ------   ------   ------   ------
Redemption fees retained by the fund..................         0.05         0.02     0.06       --       --       --
                                                             ------       ------   ------   ------   ------   ------
       Net increase/(decrease) in net assets..........         3.68        11.05     0.87     0.03    (0.16)    5.88
                                                             ------       ------   ------   ------   ------   ------
Net asset value, end of period........................       $42.23       $38.55   $27.50   $26.63   $26.60   $26.76
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
Total investment return...............................        11.00%(b)    46.89%    7.67%    4.39%    3.38%   28.76%
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------

<Caption>
RATIOS/SUPPLEMENTAL DATA:
- -------------------------
                                                                                            
Net assets, end of period (in millions).                     $ 33.4       $ 28.5   $ 18.2   $ 20.2   $ 33.5   $ 43.0
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
Ratio of expenses to average daily net assets
 (before expense reduction)...........................         1.80%(c)     1.99%    2.09%    1.83%    2.40%    2.21%
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
Ratio of expenses to average daily net assets
 (net of expense reduction)...........................         1.50%(c)     1.50%    1.50%    1.83%    2.37%    1.96%
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
Ratio of net investment income to average daily net
 assets (before expense reduction)....................         1.54%(c)     1.33%    1.96%    2.16%    3.07%    0.03%
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
Ratio of net investment income to average daily net
 assets (net of expense reduction)....................         1.84%(c)     1.82%    2.55%    2.16%    3.10%    0.28%
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
Portfolio turnover rate...............................        91.26%(b)   181.13%  179.19%  107.68%   58.99%  115.43%
                                                             ------       ------   ------   ------   ------   ------
                                                             ------       ------   ------   ------   ------   ------
</Table>

- -------------------
(a) Calculated based on the average shares outstanding during the period.

(b) Not annualized.

(c) Annualized.

                See accompanying notes to financial statements.
- --------------------------------------------------------------------------------
                                       12









- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                   NOTES TO FINANCIAL STATEMENTS (UNAUDITED)

NOTE 1. SIGNIFICANT ACCOUNTING POLICIES

    Cohen & Steers Special Equity Fund, Inc. (the fund) was incorporated under
the laws of the State of Maryland on February 14, 1997 and is registered under
the Investment Company Act of 1940, as amended, as an open-end, nondiversified
management investment company.

    The following is a summary of significant accounting policies followed by
the fund in the preparation of its financial statements. The policies are in
conformity with accounting principles generally accepted in the United States of
America. The preparation of the financial statements in accordance with
generally accepted accounting principles requires management to make estimates
and assumptions that affect the reported amounts of assets and liabilities at
the date of the financial statements and the reported amounts of income and
expenses during the reported period. Actual results could differ from those
estimates.

    Portfolio Valuation: Investments in securities that are listed on the New
York Stock Exchange are valued, except as indicated below, at the last sale
price reflected at the close of the New York Stock Exchange on the business day
as of which such value is being determined. If there has been no sale on such
day, the securities are valued at the mean of the closing bid and asked prices
for the day.

    Securities not listed on the New York Stock Exchange but listed on other
domestic or foreign securities exchanges or admitted to trading on the National
Association of Securities Dealers Automated Quotations, Inc. (Nasdaq) national
market system are valued in a similar manner. Securities traded on more than one
securities exchange are valued at the last sale price on the business day as of
which such value is being determined as reflected on the tape at the close of
the exchange representing the principal market for such securities.

    Readily marketable securities traded in the over-the-counter market,
including listed securities whose primary market is believed by Cohen & Steers
Capital Management, Inc. to be over-the-counter, but excluding securities
admitted to trading on the Nasdaq national list, are valued at the official
closing prices as reported by Nasdaq, the National Quotation Bureau, or such
other comparable sources as the board of directors deems appropriate to reflect
their fair market value. Where securities are traded on more than one exchange
and also over-the-counter, the securities will generally be valued using the
quotations the board of directors believes reflect most closely the value of
such securities.

    Unrealized gains and losses on securities that result from changes in
foreign exchange rates, as well as changes in market prices of securities, are
included in unrealized appreciation/(depreciation) on investments.

    Short-term debt securities, which have a maturity value of 60 days or less,
are valued at amortized cost, which approximates value.

    Security Transactions and Investment Income: Security transactions are
recorded on trade date. Realized gains and losses on investments sold are
recorded on the basis of identified cost. Interest income is recorded on the
accrual basis. Dividend income is recorded on the ex-dividend date. The fund
records distributions received in excess of income from underlying investments
as a reduction of cost of investments and/or realized gain. Such amounts are
based on estimates if actual amounts are not available, and actual amounts of
income, realized gain

- --------------------------------------------------------------------------------
                                       13








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

            NOTES TO FINANCIAL STATEMENTS (UNAUDITED) -- (CONTINUED)

and return of capital may differ from the estimated amounts. The fund adjusts
the estimated amounts of the components of distributions (and consequently its
net investment income) as an increase to unrealized appreciation/(deprecation)
on investment as necessary once the issuers provide information about the actual
composition of the distributions.

    Dividends and Distributions to Shareholders: Dividends from net investment
income are declared and paid semiannually. Distributions to shareholders are
recorded on the ex-dividend date. Dividends are automatically reinvested in full
and fractional shares of the fund based on the net asset value per share at the
close of business on the ex-dividend date unless the shareholder has elected to
have them paid in cash.

    A portion of the fund's dividend may consist of amounts in excess of net
investment income derived from nontaxable components of the dividends from the
fund's portfolio investments. Net realized capital gains, unless offset by any
available capital loss carryforward, are distributed to shareholders annually.

    Dividends from net investment income and capital gain distributions are
determined in accordance with U.S. federal income tax regulations, which may
differ from generally accepted accounting principles.

    Federal Income Taxes: It is the policy of the fund to qualify as a regulated
investment company, if such qualification is in the best interest of the
shareholders, by complying with the requirements of Subchapter M of the Internal
Revenue Code applicable to regulated investment companies, and by distributing
substantially all of its taxable earnings to its shareholders. Accordingly, no
provision for federal income or excise tax is necessary.

NOTE 2. INVESTMENT ADVISORY AND ADMINISTRATION FEES AND OTHER TRANSACTIONS WITH
AFFILIATES

    Investment Advisory Fees: Cohen & Steers Capital Management, Inc. (the
advisor) serves as the fund's investment advisor pursuant to an investment
advisory agreement (the advisory agreement). Under the terms of the advisory
agreement, the advisor provides the fund with the day-to-day investment
decisions and generally manages the fund's investments in accordance with the
stated policies of the fund, subject to the supervision of the fund's board of
directors. For the services provided to the fund, the advisor receives a monthly
fee in an amount equal to 1/12th of 0.90% of the average daily net assets of the
fund. For the six months ended June 30, 2004, the fund incurred $141,220 in
advisory fees.

    The investment advisor has voluntarily agreed to limit the total expenses of
the fund (excluding interest, taxes, brokerage, and extraordinary expenses) to
an annual rate of 1.50% of the fund's average net assets until December 31,
2004. As long as this expense cap continues, it may lower the fund's expenses
and increase its total return. After December 31, 2004, the expense limitation
may be terminated or revised at any time, at which time the fund's expenses may
increase and its total return may be reduced depending on the total assets of
the fund. For the six months ended June 30, 2004, the investment advisor waived
investment advisory fees of $46,890.

    Administration Fees: The fund has entered into an administration agreement
with the advisor under which the advisor performs certain administrative
functions for the fund and receives a monthly fee in an amount equal

- --------------------------------------------------------------------------------
                                       14








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

            NOTES TO FINANCIAL STATEMENTS (UNAUDITED) -- (CONTINUED)

to 1/12th of 0.02% of the fund's average daily net assets. For the six months
ended June 30, 2004, the fund paid the advisor $3,138 in fees under this
administration agreement.

    Directors' Fees: Certain directors and officers of the fund are also
directors, officers, and/or employees of the advisor. None of the directors and
officers so affiliated received compensation from the fund for their services.
For the six months ended June 30, 2004, fees and related expenses accrued for
nonaffiliated directors totaled $18,706.

    Other: At June 30, 2004, there was one investor owning 9% of the fund's
outstanding shares. Investment activities of this shareholder could have a
material impact on the fund.

NOTE 3. PURCHASES AND SALES OF SECURITIES

    Purchases and sales of securities, excluding short-term investments, for the
six months ended June 30, 2004 totaled $29,389,102 and $28,113,448,
respectively.

NOTE 4. INCOME TAXES

    At June 30, 2004, the cost of investments and net unrealized appreciation
for federal income tax purposes were as follows:

<Table>
                                                  
Aggregate cost.....................................  $28,683,355
                                                     -----------
Gross unrealized appreciation......................  $ 4,579,588
Gross unrealized depreciation......................  $  (110,133)
                                                     -----------
Net unrealized appreciation........................  $ 4,469,455
                                                     -----------
                                                     -----------
</Table>

NOTE 5. CAPITAL STOCK

    The fund is authorized to issue 50 million shares of capital stock, par
value $0.001 per share. The board of directors of the fund may increase or
decrease the aggregate number of shares of common stock that the fund has
authority to issue. Transactions in fund shares were as follows:

<Table>
<Caption>
                                       FOR THE                 FOR THE
                                  SIX MONTHS ENDED            YEAR ENDED
                                    JUNE 30, 2004         DECEMBER 31, 2003
                                ---------------------   ----------------------
                                 SHARES      AMOUNT      SHARES      AMOUNT
                                --------   ----------   --------   -----------
                                                       
Sold..........................   171,938   $6,970,474    166,537   $ 5,988,858
Issued as reinvestment of
  dividends...................     8,926      370,536     29,602     1,049,429
Redemption fees retained by
  fund(a).....................        --       40,420         --        15,331
Redeemed......................  (128,481)  (5,131,900)  (119,543)   (3,884,204)
                                --------   ----------   --------   -----------
Net increase/decrease.........    52,383   $2,249,530     76,596   $ 3,169,414
                                --------   ----------   --------   -----------
                                --------   ----------   --------   -----------
</Table>

- -------------------
(a) The fund charges a 2% redemption fee on shares sold within one year of the
    time of purchase.

- --------------------------------------------------------------------------------
                                       15








- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

            NOTES TO FINANCIAL STATEMENTS (UNAUDITED) -- (CONTINUED)

NOTE 6. BORROWINGS

    The fund, in conjunction with Cohen & Steers Realty Shares, Inc., Cohen &
Steers Institutional Realty Shares, Inc., Cohen & Steers Equity Income Fund,
Inc., Cohen & Steers Utility Fund, Inc., and Cohen & Steers Total Return Realty
Fund, Inc. has entered into a $200,000,000 credit agreement (the credit
agreement) with Fleet National Bank, as administrative agent, State Street Bank
and Trust Company, as operations agent, and the lenders identified in the credit
agreement.

    During the six months ended June 30, 2004, the fund did not utilize the line
of credit. For the six months ended June 30, 2004, the fund paid commitment fees
and other expenses of $793.

- --------------------------------------------------------------------------------
                                       16









- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

                          AVERAGE ANNUAL TOTAL RETURNS
                   (PERIODS ENDED JUNE 30, 2004) (UNAUDITED)

<Table>
<Caption>
              ONE YEAR   FIVE YEARS   SINCE INCEPTION (5/8/97)
              --------   ----------   ------------------------
                                
               36.65%      17.10%              12.27%
</Table>

The performance data quoted represents past performance. Past performance is no
guarantee of future results. The rate of return will vary and the principal
value of an investment will fluctuate and shares, if redeemed, may be worth more
or less than their original cost. Current performance may be lower or higher
than the performance data quoted. Total returns of the fund as of the most
recent month-end can be obtained by visiting our Web site at cohenandsteers.com.

    A description of the policies and procedures that the fund
    uses to determine how to vote proxies relating to portfolio
    securities is available (i) without charge, upon request, by
    calling 1-800-330-7348, (ii) on our Web site at
    cohenandsteers.com or (iii) on the Securities and Exchange
    Commission's Web site at http://www.sec.gov.

                                 PROXY RESULTS

    During the six months ended June 30, 2004, Cohen & Steers Special Equity
Fund Shares, Inc. shareholders voted on the following proposal at the
shareholder meeting held on May 25, 2004. The description of the proposal and
number of shares voted are as follows:

<Table>
                                                              SHARES VOTED   AUTHORITY
                                                                 FOR         WITHHELD
                                                                       
To elect Directors
Gregory C. Clark............................................    430,917        1,527
Bonnie Cohen................................................    430,917        1,527
Martin Cohen................................................    430,917        1,527
George Grossman.............................................    430,917        1,527
Richard J. Norman...........................................    430,917        1,527
Willard H. Smith............................................    430,917        1,527
Robert H. Steers............................................    430,917        1,527
Frank K. Ross...............................................    430,917        1,527
</Table>

- --------------------------------------------------------------------------------
                                       17









- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

              MEET THE COHEN & STEERS FAMILY OF OPEN-END FUNDS:

<Table>
                                                       
             FOR HIGH CURRENT INCOME:                                FOR TOTAL RETURN:

                 COHEN & STEERS                                       COHEN & STEERS
               EQUITY INCOME FUND                                      REALTY SHARES

      IDEAL FOR INVESTORS SEEKING A HIGH DIVIDEND         IDEAL FOR INVESTORS SEEKING MAXIMUM TOTAL
      YIELD AND CAPITAL APPRECIATION, INVESTING           RETURN THROUGH BOTH CURRENT INCOME AND
      PRIMARILY IN REITS                                  CAPITAL APPRECIATION, INVESTING PRIMARILY IN
                                                          REITS
      A, B, C AND I SHARES AVAILABLE
                                                          SYMBOL: CSRSX
      SYMBOLS: CSEIX, CSBIX, CSCIX, CSDIX
                                                          ALSO AVAILABLE: COHEN & STEERS INSTITUTIONAL
                                                          REALTY SHARES (CSRIX) REQUIRES A HIGHER
                                                          MINIMUM PURCHASE, BUT OFFERS A LOWER TOTAL
                                                          EXPENSE RATIO

                FOR TOTAL RETURN:                                  FOR CAPITAL APPRECIATION:

                 COHEN & STEERS                                         COHEN & STEERS
                  UTILITY FUND                                     SPECIAL EQUITY FUND LOGO

      IDEAL FOR INVESTORS SEEKING MAXIMUM TOTAL           IDEAL FOR INVESTORS SEEKING MAXIMUM CAPITAL
      RETURN THROUGH BOTH CURRENT INCOME AND              APPRECIATION, INVESTING IN A LIMITED NUMBER
      CAPITAL APPRECIATION, INVESTING PRIMARILY IN        OF REITS AND OTHER REAL ESTATE COMPANIES
      UTILITIES
                                                          CONCENTRATED, HIGHLY FOCUSED PORTFOLIO
      SYMBOLS: CSUAX, CSUBX, CSUCX, CSUIX
                                                          SYMBOL: CSSPX
</Table>

             FOR MORE INFORMATION ABOUT ANY COHEN & STEERS FUND
              OR TO OBTAIN A PROSPECTUS PLEASE CONTACT US AT:
         1-800-330-7348, OR VISIT OUR WEB SITE AT cohenandsteers.com

 PLEASE CONSIDER THE INVESTMENT OBJECTIVES, RISKS, CHARGES AND EXPENSES OF THE
    FUND CAREFULLY BEFORE INVESTING. A PROSPECTUS CONTAINING THIS AND OTHER
         INFORMATION ABOUT THE FUND MAY BE OBTAINED BY FOLLOWING THE
               INSTRUCTIONS ABOVE. PLEASE READ THE PROSPECTUS
                         CAREFULLY BEFORE INVESTING.

- --------------------------------------------------------------------------------
                                       18









- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.

<Table>
                                    
OFFICERS AND DIRECTORS                 KEY INFORMATION

Robert H. Steers                       INVESTMENT ADVISER
Director and chairman                  Cohen & Steers Capital Management, Inc.
                                       757 Third Avenue
Martin Cohen                           New York, NY 10017
Director and president                 (212) 832-3232

Bonnie Cohen                           FUND SUBADMINISTRATOR AND CUSTODIAN
Director                               State Street Bank and Trust Company
                                       225 Franklin Street
George Grossman                        Boston, MA 02110
Director
                                       TRANSFER AGENT
Richard J. Norman                      Boston Financial Data Services, Inc.
Director                               66 Brooks Drive
                                       Braintree, MA 02184
Frank K. Ross                          (800) 437-9912
Director
                                       LEGAL COUNSEL
Willard H. Smith Jr.                   Simpson Thacher & Bartlett LLP
Director                               425 Lexington Avenue
                                       New York, NY 10017
Adam Derechin
Vice president and assistant treasurer DISTRIBUTOR
                                       Cohen & Steers Securities, LLC
Joseph M. Harvey                       757 Third Avenue
Vice president                         New York, NY 10017

James S. Corl                          Nasdaq Symbol: CSSPX
Vice president
                                       Web site: cohenandsteers.com
Lawrence B. Stoller
Assistant secretary                    Net asset value (NAV) can be found in
                                       the daily mutual fund listings in the
                                       financial section of most major
                                       newspapers under Cohen & Steers.

                                       This report is authorized for delivery
                                       only to shareholders of Cohen & Steers
                                       Special Equity Fund, Inc. unless
                                       accompanied or preceded by the
                                       delivery of a currently effective
                                       prospectus setting forth details of
                                       the fund. Past performance, of course,
                                       is no guarantee of future results and
                                       your investment may be worth more or
                                       less at the time you sell.
</Table>

- --------------------------------------------------------------------------------
                                       19










COHEN & STEERS
SPECIAL EQUITY FUND
757 THIRD AVENUE
NEW YORK, NY 10017




     COHEN & STEERS
- -------------------------
  SPECIAL EQUITY FUND


- -------------------------
    SEMIANNUAL REPORT
      JUNE 30, 2004




                         STATEMENT OF DIFFERENCES

The division sign shall be expressed as................................. [div]
The section symbol shall be expressed as ............................... 'SS'