SELIGMAN FRONTIER FUND INC
N-30B-2, 1996-08-16
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                       SELIGMAN FINANCIAL SERVICES, INC.
                                 an affiliate of

                                     [LOGO]

                             J. & W. SELIGMAN & CO.
                                  INCORPORATED
                                ESTABLISHED 1864
                       100 PARK AVENUE, NEW YORK, NY 10017

THIS REPORT IS INTENDED ONLY FOR THE INFORMATION OF SHAREHOLDERS OR THOSE WHO
HAVE RECEIVED THE OFFERING PROSPECTUS COVERING SHARES OF CAPITAL STOCK OF
SELIGMAN FRONTIER FUND, INC., WHICH CONTAINS INFORMATION ABOUT THE SALES
CHARGES, MANAGEMENT FEE, AND OTHER COSTS. PLEASE READ THE PROSPECTUS CAREFULLY
BEFORE INVESTING OR SENDING MONEY. 

                                                                     EQFR3c 6/96
                        
- --------------------------------------------------------------------------------
                              THIRD QUARTER REPORT


- --------------------------------------------------------------------------------
                                    SELIGMAN
                                    FRONTIER
                                   FUND, INC.
- --------------------------------------------------------------------------------

                                  JUNE 30, 1996




                                     [LOGO]

- --------------------------------------------------------------------------------
                           A CAPITAL APPRECIATION FUND
                               ESTABLISHED IN 1984

<PAGE>


================================================================================
TO THE SHAREHOLDERS
- --------------------------------------------------------------------------------
Seligman Frontier Fund had a rewarding fiscal third quarter. It outpaced both
the Standard & Poor's 500 Composite Stock Price Index (S&P 500) and the Russell
2000 Index, but slightly underperformed the NASDAQ Composite Index. However, in
mid-July, the Fund, along with most equity investors, was affected by the
fluctuations in the equity markets and gave back some of its third quarter
gains.
   In the first half of 1996, the Federal Reserve Board's continuing efforts to
achieve a "soft landing" -- a healthy moderation of economic growth that does
not slip into recession -- appeared to have come to fruition. Economic data for
the second quarter of 1996 indicated continued growth in output, employment, and
incomes. More than half the early corporate earnings reports reflected the
positive effects of the strong economy, and earnings estimates rose to higher
levels. Inflation remained low and, more important, commodity price indices
declined from their recent eight-year highs, which suggested that future
inflationary pressures were in check. Overall, the economy seemed quite healthy
at the end of the second quarter.
   While fundamentals remained strong, a mid-July sell-off in the equity markets
was triggered by disappointing earnings reports from several important
technology and health care companies. This led to an overall negative assessment
that other corporate profits would fall short of expectations and economic
growth would slow, causing future earnings disappointments. Smaller-capitalized
companies were particularly affected by the broad decline in equity prices that
ensued, which was aggravated by uncertainty over the future direction of
interest rates. As your Fund invests primarily in small-cap stocks, it's
performance was impaired by the correction in the markets.
   Although the speed of such an event can unnerve even the most seasoned
investor, it is the very nature of equity markets to fluctuate over short
periods of time. Periodic corrections in stock market prices are an integral
part of US financial history -- the last significant correction in the S&P 500
was triggered by the start of the Gulf War in 1990. While viewpoints differ over
the likely direction of financial markets and the economy over the next year, we
believe that the longer-term outlook for the US economy and the equity markets
remains sound.
   We therefore must reiterate the importance of long-term investing. Since the
ups and downs of the market are unavoidable, it benefits you, our Shareholders,
to adopt a long-term investment plan whenever possible. Time is a powerful
investment tool that succeeds where market timing often fails. If you invest
over the long term, short-term market swings, while uncomfortable, have less of
an impact on your overall financial goals. As investors, you have already taken
steps to reduce your overall risk by purchasing shares of a mutual fund, which
provides portfolio diversification by investing in numerous issues and
industries.
   With the help of your investment advisor, you can formulate a long-term
investment strategy that further reduces your risk, increases your
diversification, and allows you to benefit from the advantages of mutual fund
investments.
   For specific performance information and a discussion with your Portfolio
Manager about the second quarter of 1996, your Fund's fiscal third quarter,
please refer to page 2.

By order of the Board of Directors,
/s/ William C. Morris
William C. Morris
Chairman

                                        /s/ Brian T. Zino
                                        Brian T. Zino
                                        President

July 31, 1996

                                                                               1
<PAGE>

================================================================================
INTERVIEW WITH YOUR PORTFOLIO MANAGER
- --------------------------------------------------------------------------------
ARSEN MRAKOVCIC

HOW DID SELIGMAN FRONTIER FUND PERFORM IN THE PAST THREE MONTHS?
In the second quarter of 1996, the Fund's third quarter, Seligman Frontier Fund
outpaced the Standard & Poor's 500 Composite Stock Price Index and the Russell
2000 Index, but slightly underperformed the NASDAQ Composite Index.

WHAT MARKET FACTORS AFFECTED THE FUND IN THE PAST THREE MONTHS?
The strong economic data that was issued in the second quarter produced fears of
inflation, which affected both the bond and equity markets. The stock market,
which had been rallying for the last 16 months and had gotten ahead of itself in
the short term, experienced weakness in May because of the bond market sell-off
and the increase in interest rates. In response to this market environment, and
in keeping with our valuation discipline, we positioned the Fund away from the
expensively priced sectors. Consequently, Seligman Frontier Fund was somewhat
protected from the market weakness that began at the end of May and continued
into June and July.

WHAT INDUSTRIES, SPECIFICALLY, PERFORMED WELL WITHIN THE PORTFOLIO?
Radio broadcasting continued to be a very strong group, after a rewarding 1995.
With the passage of the 1996 Telecommunications Deregulation Act, which greatly
increased a single owner's maximum ownership level, industry consolidation
escalated. For example, Jacor Communications, one of the Fund's largest radio
broadcasting holdings, has been aggressively acquiring radio properties in 1996.
Consolidation can bring greater control of local markets and increased pricing
power and revenue prospects.

WHAT CHANGES DID YOU MAKE IN THE PORTFOLIO?
This past quarter, our overall exposure to technology dropped to approximately
16% of the portfolio. This resulted from our cautious investment stance, as we
sold certain technology issues with weakening fundamentals. While the technology
sector remains a good long-term investment for growth-oriented investors, we
have witnessed some short-term volatility in certain industries including
semiconductors and semiconductor capital equipment. The current volatility has
deflated valuations, giving us an opportunity to purchase reasonably priced
issues with strong long-term fundamentals. We believe that it is in the interest
of our shareholders to continue to own the better managed market share leaders
in this industry.

WHAT IS YOUR OUTLOOK FOR THE FUND?
Overall, the economy seems to be on track, which has been particularly
beneficial for small- capitalized stocks, and consequently the Fund. The recent
weakness in the market will undoubtedly provide opportunities to buy strong
companies at reasonable prices. Going forward, we will continue to focus on
individual stock selection, looking at reasonably valued companies with strong
managements and good market positions within growing industries. This approach
seems to be the best antidote for most market ailments.

2
<PAGE>

================================================================================
SELIGMAN FRONTIER FUND, INC.
- --------------------------------------------------------------------------------

INVESTMENT RESULTS
TOTAL RETURNS*
FOR PERIODS ENDED JUNE 30, 1996

<TABLE>
<CAPTION>
                                                                                     AVERAGE ANNUAL
                                                                 -------------------------------------------
                              CLASS B                                                               CLASS D
                               SINCE                                                                 SINCE
                             INCEPTION    THREE       SIX          ONE        FIVE        TEN      INCEPTION
                              4/22/96    MONTHS      MONTHS       YEAR        YEARS      YEARS      5/3/93
                           -----------  --------  ----------    -------     -------    -------      -----
<S>                           <C>         <C>         <C>         <C>         <C>        <C>         <C>   
CLASS A
With Sales Charge               n/a       1.92%        7.68%      23.46%      23.31%     13.77%       n/a
Without Sales Charge            n/a       7.01        13.05       29.57       24.51      14.32        n/a
CLASS B
With 5% CDSL                  (2.94)%      n/a         n/a         n/a         n/a        n/a         n/a
Without CDSL                   2.06        n/a         n/a         n/a         n/a        n/a         n/a
CLASS D
With 1% CDSL                    n/a       5.83        11.67       27.68        n/a        n/a         n/a
Without CDSL                    n/a       6.83        12.67       28.68        n/a        n/a        26.34%
RUSSELL 2000**                (0.33)++    5.00        10.36       23.89       17.51      10.42       16.72+
</TABLE>

NET ASSET VALUE PER SHARE
<TABLE>
<CAPTION>
                                JUNE 30, 1996              MARCH 31, 1996             DECEMBER 31, 1995
                               --------------             ----------------          --------------------
<S>                                <C>                          <C>                        <C>   
CLASS A                            $15.42                       $14.41                     $13.64
CLASS B                             14.85                        14.55+++                   n /a
CLASS D                             14.85                        13.90                      13.18
</TABLE>

CAPITAL GAIN INFORMATION
FOR THE NINE MONTHS ENDED JUNE 30, 1996
                                              CAPITAL GAIN
                                -----------------------------------------
                                   REALIZED                  UNREALIZED0
                                --------------             --------------
CLASS A                             $0.693                     $2.051
CLASS B                              0.693                      2.051
CLASS D                              0.693                      2.051

  * Return figures reflect any change in price per share and assume the
    reinvestment of dividends and capital gain distributions. Return figures for
    Class A shares are calculated without and with the effect of the initial
    4.75% maximum sales charge. Class A share returns reflect the effect of the
    0.25% Administration, Shareholder Services and Distribution Plan after June
    1, 1992, only. Returns for Class B shares are calculated without and with
    the effect of the maximum 5% contingent deferred sales load ("CDSL"),
    charged only on certain redemptions made within one year of the date of
    purchase, declining to 1% in the sixth year and 0% thereafter. Returns for
    Class D shares are calculated without and with the effect of the 1% CDSL,
    charged only on redemptions made within one year of the date of purchase.
    The rates of return will vary and the principal value of an investment will
    fluctuate. Shares, if redeemed, may be worth more or less than their
    original cost. Past performance is not indicative of future investment
    results.
 ** The Russell 2000 is an unmanaged index that assumes reinvestment of
    estimated dividends and does not reflect fees and expenses. Investors may
    not invest directly in an index.
  0 Represents the per share amount of net unrealized appreciation of portfolio 
    securities as of June 30, 1996.
  + From April 30, 1993.
 ++ From April 30, 1996.
+++ As of April 22, 1996.

                                                                               3
<PAGE>

================================================================================
SELIGMAN FRONTIER FUND, INC.
- --------------------------------------------------------------------------------
LARGEST PORTFOLIO CHANGES
DURING PAST THREE MONTHS
                                         SHARES
                                 ----------------------
                                              HOLDINGS
ADDITIONS                         INCREASE     6/30/96
- ----------                       ----------  ----------
AccuStaff ...................     300,000     300,000
American HomePatient ........     160,500     160,500
CMACInvestment ..............     125,000     125,000
CompuServe ..................     280,000     280,000
DST Systems .................     175,000     440,000
Friedman's (Class A) ........     250,000     250,000
General Nutrition ...........     475,000     475,000
Genesis Health Ventures .....     200,000     200,000
Scherer (R.P.) ..............     185,000     325,000
Watson Pharmaceuticals ......     205,000     405,000


                                              HOLDINGS
REDUCTIONS                        DECREASE     6/30/96
- --------------                   ----------  ----------
Buckeye Cellulose ...........     175,000     100,000
Clintrials Research .........     100,000          --
ContiFinancial ..............     150,000          --
Longhorn Steaks .............     115,000     300,000
Microchip Technology ........     160,000          --
National Surgery Centers ....      60,000     150,000*
Oakley ......................     145,000     250,000
SITEL .......................      65,000          --
Tencor Instruments ..........     200,000          --
United Video Satellite Group
   (Class A) ................     125,000          --

Largest portfolio changes from the previous quarter to the current quarter are
based on cost of purchases and proceeds from sales of securities.

* Includes 50,000 shares received as a result of a 3-for-1 stock split. 


MAJOR PORTFOLIO HOLDINGS
AT JUNE 30, 1996

SECURITY                                      VALUE
- --------                                   -----------
CalEnergy ..........................       $17,850,000
Corporate Express ..................        17,226,875
BDM International ..................        16,275,000
Watson Pharmaceuticals .............        15,339,375
Total Renal Care Holdings ..........        15,210,000
Scherer (R.P.) .....................        14,746,875
United Transnet ....................        14,651,875
DST Systems ........................        14,080,000
UCAR International .................        13,111,875
Ceridian ...........................        12,877,500


MAJOR SECTORS
AT JUNE 30, 1996

[THE FOLLOWING PLOT POINTS REPRESENTS A PIE CHART IN THE PRINTED REPORT.]

Business Goods and Services ...........................................    16.6%
Drugs and Health Care .................................................    11.9%
Financial Services ....................................................     6.9%
Electronics ...........................................................     6.3%
Capital Goods .........................................................     5.7%
Computer Software and  Services .......................................     5.3%
Medical Products and  Technology ......................................     5.0%
Media and Broadcasting ................................................     4.2%
Communications ........................................................     4.1%
Consumer Goods  and Services ..........................................     3.3%
Retail Trade ..........................................................     3.3%
Other .................................................................    27.4%

4
<PAGE>

================================================================================
PORTFOLIO OF INVESTMENTS (unaudited)                               June 30, 1996
- --------------------------------------------------------------------------------
                                                     SHARES           VALUE
                                                    --------         -------
COMMON STOCKS 92.4%
ADVERTISING 1.1%
Heritage Media (Class A)* .................          168,000       $  6,699,000
Katz Media Group* .........................          180,000          2,587,500
                                                                   ------------
                                                                      9,286,500
                                                                   ------------
AEROSPACE AND
   DEFENSE 3.1%
Avondale Industries* ......................          540,000          9,686,250
BDM International* ........................          350,000         16,275,000
                                                                   ------------
                                                                     25,961,250
                                                                   ------------
APPAREL 0.8%
St. John Knits ............................          147,000          6,559,875
                                                                   ------------
BUSINESS GOODS AND
   SERVICES 16.8%
AccuStaff* ................................          300,000          8,212,500
Affiliated Computer Services
   (Class A)* .............................           55,500          2,615,437
Bell & Howell Holdings* ...................          244,600          7,980,075
BISYS Group* ..............................          195,000          7,324,687
Ceridian* .................................          255,000         12,877,500
Corporate Express* ........................          430,000         17,226,875
DST Systems* ..............................          440,000         14,080,000
Fair Isaac ................................           60,000          2,655,000
Inter-Tel* ................................          450,000         11,812,500
May & Speh* ...............................          306,000          4,743,000
National Data .............................          300,000         10,275,000
Nu-Kote Holdings (Class A)* ...............          310,000          5,095,625
Personnel Group of America* ...............          125,000          3,078,125
Profit Recovery Group
   International* .........................          136,000          2,703,000
SPS Transaction Services* .................          100,000          1,800,000
US Office Products* .......................          225,000          9,421,875
United Transnet ...........................          595,000         14,651,875
Wilmar Industries* ........................          155,000          3,952,500
                                                                   ------------
                                                                    140,505,574
                                                                   ------------
CAPITAL GOODS 5.8%
Carbide/Graphite Group* ...................          475,000          8,757,812
DT Industries .............................          150,000          2,756,250
Fusion Systems* ...........................          110,000          2,777,500
Greenfield Industries .....................          200,000          6,650,000
Oak Industries* ...........................          300,000          8,887,500
UCAR International* .......................          315,000         13,111,875
Wolverine Tube* ...........................          150,000          5,250,000
                                                                   ------------
                                                                     48,190,937
                                                                   ------------
COMMUNICATIONS 4.2%
Arch Communications Group* ................          250,000          4,625,000
CIDCO* ....................................          240,000          8,460,000
Glenayre Technologies* ....................          200,000          9,987,500
MobileMedia (Class A)* ....................          150,000          1,800,000
Omnipoint* ................................          250,000          6,515,625
ProNet* ...................................           79,000            972,687
Western Wireless (Class A)* ...............          126,750          2,733,047
                                                                   ------------
                                                                     35,093,859
                                                                   ------------
COMPUTER HARDWARE/
   PERIPHERALS 2.2%
Electronics for Imaging* ..................          175,000         12,151,563
Planar System* ............................          418,000          5,930,375
                                                                   ------------
                                                                     18,081,938
                                                                   ------------
COMPUTER SOFTWARE AND
   SERVICES 5.3%
CompuServe* ...............................          280,000          5,915,000
Control Data Systems* .....................          430,000          9,218,125
Mentor Graphics* ..........................          525,000          8,498,437
MetroMail * ...............................          250,000          5,593,750
SunGard Data Systems* .....................          125,000          5,007,812
Synopsys * ................................          260,000         10,367,500
                                                                   ------------
                                                                     44,600,624
                                                                   ------------
CONSTRUCTION AND
   SERVICES 1.4%
AMRE* .....................................          520,000         11,375,000
                                                                   ------------
CONSUMER GOODS AND
   SERVICES 3.3%
Barefoot ..................................          290,000          3,153,750
Buckeye Cellulose* ........................          100,000          2,762,500
HFS* ......................................          147,600         10,332,000
Oakley* ...................................          250,000         11,375,000
                                                                   ------------
                                                                     27,623,250
                                                                   ------------
DRUGS AND HEALTH
   CARE 12.1%
American HomePatient* .....................          160,500          7,062,000
AmeriSource Health (Class A)* .............          260,000          8,645,000
Community Psychiatric Centers .............          485,000          4,607,500
Genesis Health Ventures* ..................          200,000          6,275,000
National Surgery Centers* .................          150,000          4,068,750
Omnicare ..................................          370,000          9,805,000
Protein Design Labs* ......................          100,000          2,237,500
RISCORP (Class A)* ........................           50,000            900,000
Schein (Henry)* ...........................          100,000          3,818,750
Scherer (R.P.)* ...........................          325,000         14,746,875
Total Renal Care Holdings* ................          360,000         15,210,000
Vivra* ....................................          250,000          8,218,750
Watson Pharmaceuticals* ...................          405,000         15,339,375
                                                                   ------------
                                                                    100,934,500
                                                                   ------------

ELECTRONICS 6.4%
Cognex* ...................................          645,000         10,521,562
Credence Systems* .........................          250,000          3,359,375
Electro Scientific Industries* ............          132,500          2,732,813
Electroglas* ..............................          239,000          3,390,813
Lattice Semiconductor* ....................          190,000          4,583,750
Maxim Intergrated Products ................          200,000          5,462,500
Sanmina* ..................................          230,000          6,210,000
Ultratech Stepper* ........................           92,500          1,728,594
Vicor* ....................................          400,000          9,325,000
Zilog* ....................................          250,000          6,000,000
                                                                   ------------
                                                                     53,314,407
                                                                   ------------

                                                                               5
<PAGE>

================================================================================
PORTFOLIO OF INVESTMENTS (unaudited) (continued)                   June 30, 1996
- --------------------------------------------------------------------------------
                                                     SHARES           VALUE
                                                    --------         -------
FARM EQUIPMENT 0.6%
AGCO ......................................          185,000       $  5,133,750
                                                                   ------------
FINANCIAL SERVICES 7.0%
CMAC Investment ...........................          125,000          7,187,500
Commerce Bancorp ..........................          145,750          3,443,344
First Investors Financial
   Services Group* ........................          150,000          1,678,125
First Savings Bank of
   Washington .............................          150,000          2,334,375
Flushing Financial* .......................          150,000          2,568,750
GCR Holdings ..............................          210,000          5,538,750
Jayhawk Acceptance* .......................          350,000          4,834,375
Klamath First Bancorp .....................          150,000          2,184,375
Leasing Solutions* ........................          230,000          3,565,000
Meadowbrook Insurance Group ...............          295,100          9,074,325
PFF Bancorp* ..............................          100,000          1,100,000
T. Rowe Price .............................          230,000          7,101,250
Roosevelt Financial Group .................          300,000          5,793,750
Statewide Financial* ......................          150,000          1,828,125
                                                                   ------------
                                                                     58,232,044
                                                                   ------------
FOOD AND BEVERAGES 0.7%
Canandaigua Wine (Class A)* ...............          200,000          6,025,000
                                                                   ------------
GAMING 1.3%
GTECH Holdings* ...........................          350,000         10,368,750
                                                                   ------------
MANUFACTURING 0.5%
American Homestar* ........................          175,000          4,462,500
                                                                   ------------
MEDIA AND
  BROADCASTING 4.3%
Argyle Television (Class A)* ..............          340,000          8,415,000
Chancellor Broadcasting
   (Class A)* .............................          175,000          5,501,563
Evergreen Media (Class A)* ................          225,000          9,562,500
Jacor Communications* .....................          230,000          7,144,375
Paxson Communications
   (Class A)* .............................          500,000          5,312,500
                                                                   ------------
                                                                     35,935,938
                                                                   ------------
MEDICAL PRODUCTS AND
   TECHNOLOGY 5.1%
CompDent* .................................         150,000           6,956,250
Dentsply International ....................         290,000          12,270,625
Rural/Metro* ..............................         202,300           6,903,488
Sybron International* .....................         325,000           8,125,000
Waters* ...................................         250,000           8,250,000
                                                                   ------------
                                                                     42,505,363
                                                                   ------------
OIL AND GAS 1.6%
Pogo Producing ............................         200,000           7,625,000
Santa Fe Energy Resources .................         500,000           5,937,500
                                                                   ------------
                                                                     13,562,500
                                                                   ------------

                                                   SHARES OR
                                                   PRIN. AMT.
                                                   ----------   
PUBLISHING 0.6%
World Color Press* ........................         201,800shs.       5,120,675
                                                                   ------------
RESTAURANTS 0.9%
Longhorn Steaks* ..........................         300,000           7,425,000
                                                                   ------------
RETAIL TRADE 3.3%
Casey's General Stores ....................         350,000           6,912,500
Consolidated Stores* ......................         100,000           3,675,000
Friedman's (Class A)* .....................         250,000           6,406,250
General Nutrition* ........................         475,000           8,282,813
Saks Holdings* ............................          66,000           2,252,250
                                                                   ------------
                                                                     27,528,813
                                                                   ------------
SPECIALTY CHEMICALS 1.9%
Minerals Technologies .....................         250,000           8,562,500
Sealed Air * ..............................         215,000           7,229,375
                                                                   ------------
                                                                     15,791,875
                                                                   ------------
UTILITIES/IPP 2.1%
CalEnergy* ................................         700,000          17,850,000
                                                                   ------------
TOTAL COMMON STOCKS
   (Cost $658,693,669) ....................                         771,469,922
                                                                   ------------

SHORT-TERM HOLDINGS 9.0%
Bank of Montreal, Toronto
   Fixed Time Deposit,
   5 3/8%, 7/1/96 .........................    $37,200,000
                                                                     37,200,000
National Westminster Bank,
   Nassau Fixed Time
   Deposit, 5 1/2%, 7/1/96 ................     38,000,000           38,000,000
                                                                   ------------
TOTAL SHORT-TERM HOLDINGS
   (Cost $75,200,000) .....................                          75,200,000
                                                                   ------------
TOTAL INVESTMENTS 101.4%
   (Cost $733,893,669) ....................                        $846,669,922

OTHER ASSETS LESS
   LIABILITIES (1.4)% .....................                         (11,437,191)
                                                                   ------------
NET ASSETS 100.0% .........................                        $835,232,731
                                                                   ============

- ----------
* Non-income producing security.

Note: Investments in stocks are valued at current market values or, in their
absence, at fair value determined in accordance with procedures approved by the
Board of Directors. Securities traded on national exchanges are valued at last
sales prices or, in their absence and in the case of over-the-counter
securities, a mean of bid and asked prices.
Short-term holdings maturing in 60 days or less are valued at amortized cost.

6



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