<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


[X]         QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(d) OF THE
                       SECURITIES EXCHANGE ACT OF 1934

For the Quarterly Period Ended      September 30, 1997
                               -------------------------------------

                                       OR

[ ]         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                      SECURITIES EXCHANGE ACT OF 1934

For the transition period from                  to
                                ---------------     ----------------

Commission file number              0-21682
                        --------------------------------------------

                                  SPARTA, Inc.
-------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

          Delaware                                     63-0775889
-------------------------------                     -----------------
(State or other jurisdiction of                     (I.R.S. Employer)
 incorporation or organization)

       23041 Avenida de la Carlota, Suite 325, Laguna Hills, CA 92653-1595
-------------------------------------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (714) 768-8161
-------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)

                                 Not Applicable
-------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act or 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports) and (2) has been subject to such filing
requirements for the past 90 days.

Yes   x     No
    -----       -----

As of October 3, 1997, the registrant had 5,691,135 shares of common stock, $.01
par value per share, issued and outstanding.


<PAGE>   2


                                  SPARTA, Inc.

            QUARTERLY REPORT FOR THE PERIOD ENDED SEPTEMBER 30, 1997

                                      INDEX


PART I            FINANCIAL STATEMENTS

ITEM 1            Quarterly Financial Statements

                  Statements of Income for the Nine Months Ended September 30,
                  1997 and September 30, 1996 (Unaudited)

                  Balance Sheets as of September 30, 1997 and December 31, 1996
                  (Unaudited)

                  Statement of Cash Flows for the Nine Months Ended September
                  30, 1997 and September 30, 1996 (Unaudited)

                  Notes to Consolidated Financial Statements (Unaudited)

ITEM 2            Management's Discussion and Analysis of Financial Condition
                  and Results of Operations


PART II  OTHER INFORMATION

ITEM 1            LEGAL PROCEEDINGS

                  The Company has no investigations, claims, and lawsuits
                  arising out of its business, nor any known to be pending.

ITEM 2            CHANGES IN SECURITIES

                  Not Applicable

ITEM 3            DEFAULTS UPON SENIOR SECURITIES

                  Not Applicable

ITEM 4            SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

                  None in fiscal quarter for which this report is filed.

ITEM 5            OTHER MATERIALLY IMPORTANT EVENTS

                  Not Applicable

ITEM 6            EXHIBITS AND REPORTS ON FORM 8-K

                  No report(s) on Form 8-K were filed by the Company during the
                  fiscal quarter for which this report is filed.

EXHIBIT 11        Computations of Earnings per Share



<PAGE>   3




                                     PART I


                              FINANCIAL INFORMATION




<PAGE>   4

CONSOLIDATED STATEMENT OF INCOME
(UNAUDITED)

ITEM 1.  FINANCIAL STATEMENTS
-----------------------------
<TABLE>
<CAPTION>


                                             THREE MONTHS ENDED SEPTEMBER 30         NINE MONTHS ENDED SEPTEMBER 30
                                          --------------------------------------  --------------------------------------
                                                1997                1996                1997                 1996
                                          ------------------  ------------------  ------------------   -----------------

<S>                                      <C>                 <C>                 <C>                 <C>        
SALES                                     $       23,408,000  $       17,817,000  $       63,519,000   $      50,981,000
                                          ------------------  ------------------  ------------------   -----------------

COSTS AND EXPENSES:

  Labor costs and related benefits                12,316,000           8,640,000          33,342,000          25,275,000

  Subcontractor & other costs                      7,121,000           5,336,000          17,271,000          13,608,000

  Facility costs                                   1,620,000           1,679,000           5,157,000           5,149,000

  Travel and other                                   328,000             936,000           2,068,000           2,887,000

  Interest expense, net                               26,000              (6,000)            134,000              34,000
                                          ------------------  ------------------  ------------------   -----------------

                                                  21,411,000          16,585,000          57,972,000          46,953,000
                                          ------------------  ------------------  ------------------   -----------------

INCOME BEFORE PROVISION FOR
  TAXES ON INCOME                                  1,997,000           1,232,000           5,547,000           4,028,000

PROVISION FOR TAXES ON INCOME                        839,000             518,000           2,330,000           1,692,000
                                          ------------------  ------------------  ------------------   -----------------

NET INCOME                                $        1,158,000  $          714,000  $        3,217,000   $       2,336,000
                                          ==================  ==================  ==================   =================

EARNINGS PER SHARE(1)                     $             0.15  $             0.09  $             0.41   $            0.33
                                          ==================  ==================  ==================   =================

</TABLE>

(1) Earnings per shares adjusted for interest and accretion - See Exhibit 11






     The accompanying notes are an integral part of the financial statements


<PAGE>   5




CONSOLIDATED BALANCE STATEMENT
(UNAUDITED)
<TABLE>
<CAPTION>

                                                                    SEPTEMBER 30, 1997         DECEMBER 31, 1996
                                                                   ---------------------      --------------------
                                                                       (Unaudited)                 (Audited)
<S>                                                               <C>                       <C>    
ASSETS

CURRENT ASSETS
  Cash                                                             $            182,000       $           151,000
  Accounts receivable                                                        21,405,000                21,160,000
  Prepaid expenses                                                              295,000                   306,000
                                                                   --------------------       -------------------
    TOTAL CURRENT ASSETS                                                     21,882,000                21,617,000
  Equipment and improvements, net                                             6,967,000                 6,028,000
  Other assets                                                                1,546,000                 1,409,000
                                                                   --------------------       ------------------- 

                                                                   $         30,395,000       $        29,054,000
                                                                   ====================       =================== 

LIABILITIES AND STOCKHOLDERS' EQUITY
CURRENT LIABILITIES
  Accrued compensation                                             $          5,098,000       $         3,871,000
  Accounts payable and other accrued expenses                                 1,932,000                 3,320,000
  Current portion of notes payable                                            1,262,000                   461,000
  Current portion of subordinated debt                                          493,000                   640,000
  Income tax payable                                                                  0                   466,000
  Deferred income taxes                                                       2,283,000                 2,849,000
                                                                   --------------------       ------------------- 
    TOTAL CURRENT LIABILITIES                                                11,068,000                11,607,000

NOTES PAYABLE
SUBORDINATED NOTES PAYABLE                                                      761,000                 1,090,000
DEFERRED INCOME TAXES                                                         2,618,000                 2,828,000

REDEEMABLE PREFERRED STOCK
  Preferred stock, $.01 par value; 2,000,000 shares
  authorized; 569,039 and
  569,039 shares issued and outstanding                                       3,915,000                 3,044,000
STOCKHOLDERS' EQUITY
  Common stock, $.01 par value, 25,000,000 shares authorized; 
  13,422,395 and 12,376,781 shares issued and outstanding                       134,000                   124,000
  Additional paid-in capital                                                 25,616,000                22,229,000
  Retained earnings                                                          23,276,000                20,929,000
  Treasury stock                                                            (36,993,000)              (32,797,000)
                                                                   --------------------       ------------------- 
    TOTAL STOCKHOLDERS' EQUITY                                               12,033,000                10,485,000
                                                                   --------------------       ------------------- 

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                         $         30,395,000       $        29,054,000
                                                                   ====================       =================== 

</TABLE>






     The accompanying notes are an integral part of the financial statements



<PAGE>   6
CONSOLIDATED STATEMENT OF CASH FLOWS
(UNAUDITED)

<TABLE>
<CAPTION>
                                                                           NINE MONTHS ENDED SEPTEMBER 30,
                                                                     ---------------------------------------------
                                                                             1997                     1996
                                                                     ----------------------    -------------------

<S>                                                                    <C>                       <C>             
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net Income                                                           $         3,217,000       $      2,336,000
  Adjustments to reconcile net income to net
    cash provided by operating activities:
      Depreciation and amortization                                              1,134,000              1,153,000
      Loss on sale of equipment                                                    105,000                106,000
      Employee compensation paid in stock                                        1,690,000              1,334,000
      Changes in assets and liabilities:
        Accounts receivable                                                       (245,000)             1,755,000
        Prepaid expenses                                                            11,000                (78,000)
        Other assets                                                              (137,000)               778,000
        Accrued compensation                                                     1,227,000              1,023,000
        Accounts payable and other accrued expense                              (1,388,000)               185,000
        Income taxes payable                                                      (393,000)               685,000
        Deferred income taxes                                                     (849,000)              (849,000)
      Tax benefit relating to stock plan                                            84,000                  7,000
                                                                       -------------------       ----------------
          NET CASH PROVIDED BY OPERATING ACTIVITIES                              4,456,000              8,435,000
                                                                       -------------------       ----------------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Capital expenditures                                                        (2,178,000)            (1,150,000)
                                                                       -------------------       ----------------
          NET CASH USED IN INVESTING ACTIVITIES                                 (2,178,000)            (1,150,000)

CASH FLOWS FROM FINANCING ACTIVITIES:
  Proceeds from issuance of redeemable preferred stock                                   0                900,000
  Proceeds from issuance of stock                                                1,622,000                305,000
  Cash purchases of treasury stock                                              (3,785,000)            (2,462,000)
  Net (repayments) proceeds line-of-credit agreement                               802,000               (942,000)
  Principal payments on debt                                                      (886,000)            (1,004,000)
                                                                       -------------------       ----------------
          NET CASH USED IN FINANCING ACTIVITIES                                 (2,247,000)            (3,203,000)
                                                                       -------------------       ----------------

NET INCREASE IN CASH                                                                31,000              4,082,000
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                                   151,000                222,000
                                                                       -------------------       ----------------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                                         182,000              4,304,000
                                                                       ===================       ================

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION: 
  Cash paid during the period
  for:
    Interest                                                           $          134,000        $        34,000
                                                                       ==================        ===============
    Income taxes                                                       $        3,494,000        $     1,856,000
                                                                       ==================        ===============

</TABLE>




     The accompanying notes are an integral part of the financial statements



<PAGE>   7

                                  SPARTA, INC.

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                   ------------------------------------------
                                   (Unaudited)


NOTE A - BASIS OF PRESENTATION
------------------------------

The accompanying financial information has been prepared in accordance with the
instructions to Form 10-Q and therefore does not necessarily include all
information and footnotes necessary for a fair presentation of financial
position, results of operations and cash flows in conformity with generally
accepted accounting principles.

The Company's fiscal year is the 52 or 53 week period ending on the Friday
closest to December 31. The Company's last fiscal year ended on January 3, 1996;
and, its third quarter ended October 3, 1997 and corresponding third quarter
last year on September 27, 1996. To aid the reader of the financial statements,
the year end has been presented as December 31, 1996 and the quarters and nine
months ended September 30, 1996 and September 30, 1997.

In the opinion of management, the unaudited financial information for the
nine-month period ended September 30, 1997 and September 30, 1996 reflects all
adjustments (which include only normal, recurring adjustments) necessary for a
fair presentation thereof.

NOTE B - RECEIVABLES
--------------------

Unbilled accounts receivable include $1,422,000 of costs incurred on projects
for which the Company has been requested by the customer to begin work under a
new contract or extend work under a present contract, but for which final
contract negotiations or formal contracts or contract modifications have not
been executed at September 30, 1997.

NOTE C - INCOME TAXES
---------------------

Income taxes for interim periods are computed using the estimated annual
effective rate method.



<PAGE>   8



ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
          RESULTS OF OPERATIONS

The Management Discussion and Analysis of Financial Condition and Results of
Operation may contain forward-looking statements that involve risks and
uncertainties. The Company's actual results may differ significantly from
projections contained in forward-looking statements. For a more complete
discussion of the factors which could cause such a difference, the Company's
Form 10-K for the year ended December 31, 1996, should be consulted.

The following table sets forth, for the periods indicated, selected financial
results from the Company's continuing operations and audited Financial
Statements.

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                        For three months ended Sept. 30,  For nine months ended Sept. 30,
                                        --------------------------------  -------------------------------
                                             1997             1996             1997             1996
                                        -------------      ------------   ------------      -------------
<S>                                     <C>                 <C>            <C>               <C>
Sales                                      23,408,000        17,817,000     63,519,000         50,981,000
Gross profit(1)                             1,967,000         1,469,000      5,919,000          4,680,000
Gross profit as a % of costs                     9.17%             8.99%         10.28%             10.11%
Net income(2)                               1,158,000           714,000      3,217,000          2,336,000
Number of staff                                   610               479            610                479
</TABLE>

<TABLE>
<CAPTION>
                                                                         Balance at
                                                --------------------------------------------------------------
                                                Sept. 30, 1997          Dec. 31, 1996           Sept. 30, 1996
                                                --------------          -------------           --------------
<S>                                             <C>                     <C>                     <C>
Funded 12 month backlog                             37,500,000             36,200,000               27,300,000
Total 12 month contract backlog                     92,200,000             76,400,000               67,200,000
Stockholders equity                                 12,032,000             10,722,000               10,576,000
Equity per common share                                   1.92                   1.67                     1.65     
Stock repurchase notes                               1,255,000              1,730,000                1,956,000
Line of credit                                       1,262,000                476,000                        0
Number in days sales in receivables                         83                    109                       86
Current ratio                                              2.0                    1.8                      1.9
</TABLE>

(1)    The company defines gross profits as sales less costs and expenses
       excluding interest costs and certain expenses which cannot be billed to
       its government customers.

(2)    Prior to adjustments for interest and accretion on stock - See Exhibit 1

REVENUES

The Company's contract revenues for the 3rd quarter were up 31.4% from the
corresponding three month period in 1996. Third quarter sales of $23,408,000
were the highest quarterly total in the Company's history. Profitability for the
three month period ended September 30, 1997 was up 33.9% when compared to the
corresponding period in 1996. Profitability as a percent of costs increased to
9.2% from 9.0% for the corresponding period in 1996, and continues to represent
historical levels of profitability. Borrowings against the Company's line of
credit totaled $1,262,000 as of the end of the 3rd quarter compared to a
borrowing level of zero at the end of the corresponding period in 1996.

ANNUALIZED BACKLOG

During the 3rd quarter, the Company had three major competitive losses: MICOM
Information Management, a $50,000,000 contract over 5 years; AFOTEC, a
$16,000,000 contract over 5 years; and SSES, a $10,000,000 contract over 5
years. The MICOM Information Management and the SSES contracts were bid as
subcontractors to SAIC and Sheppa, respectively, whereas SPARTA bid the AFOTEC
contract as the prime contractor. The Company also had two major competitive
wins during the quarter: TSMO, a $79,000,000 contract over 5 years and BMD Cost
Analysis, a $4,000,000 contract over 5 years. The Company is the prime
contractor for TSMO and is a subcontractor to MCR for the 



<PAGE>   9


BMD Cost Analysis Contract. Although large, the TSMO contract will have minimal
contribution to contract backlog because first year funding on that contract is
expected to be small. The Company increased its annualized contract backlog in
the 3rd quarter from $86,800,000 to $92,200,000. Further near-term growth in
contract backlog is not expected based on the projected award dates of the
proposals outstanding and the number of proposals expected in the near term.
From the beginning of the year, the Company has increased its contract backlog
by approximately $16,000,000.

LIQUIDITY AND CAPITAL RESOURCES

The Company's primary sources of liquidity are funds provided by operations and
the bank line of credit. The line of credit provides for borrowings up to
$10,000,000 with all borrowing due December 1, 1997. Borrowings under the line
of credit at September 30, 1997 totaled $1,262,000. The Company has negotiated
its bank line of credit requirements for 1998 and 1999, and expects to have the
agreement in place in the 4th quarter.

STOCKHOLDER EQUITY

The Company increased stockholder's equity 12.2% year to date from $10,722,000
at December 31, 1996 to $12,032,000 at September 30, 1997. Equity increased 4.9%
in the 3rd quarter from $11,469,000 at June 30, 1997 to $12,032,000 at September
30, 1997.

STOCK PURCHASE AGREEMENT

In November, 1994, the Company entered into a Stock Purchase Agreement (the
"Agreement") with Science Applications International Corporation ("SAIC"), under
which SAIC agreed to purchase, during the first year of the Agreement, Preferred
Stock of the Company with an aggregate price of $1,200,000. Under the Agreement,
SAIC also has the option, but not the obligation, to buy additional shares of
Preferred Stock. The Agreement also grants SAIC the option to require the
Company to repurchase all of the Preferred Stock held by SAIC at the Formula
Price at time of option exercise. In the event the option is exercised, the
Company may issue SAIC a subordinated note bearing an interest rate equal to the
lesser of prime or 10%. SAIC suspended its purchase of Company Preferred Stock
in the 4th quarter of 1996. The total purchase to September 30, 1997 of
$2,400,000 of Company Preferred Stock represents 9.19% of the Company's
outstanding stock. Through September 30, 1997 accretion of Preferred Stock was
$1,515,000.

STOCK REPURCHASE PROGRAM

The Company continues to conduct its stock repurchase program, under which the
Company repurchases shares of the Company's stock desired to be sold by the
Company's existing stockholders. All such stock repurchases (whether from
terminating employees or others) are subject to quarterly restrictions which are
designed to insure that the Company's liquidity and equity are not materially
impaired. The Company's stock price is determined by a formula. Under the
current Formula Price for pricing stock, liquidity is not a factor in the
equation. However, during any extended period of non-liquidity, the Board of
Directors may make a change in the stock price formula to factor in the lack of
liquidity. The Formula Price is reviewed periodically by an independent stock
appraiser to assure the Board of Directors that the stock price formula is
calculating a price within a reasonable fair market price range. All appraisals
to date have shown the stock price calculated by the current formula to fall
within a fair and reasonable price range as compared with publicly held
companies of similar size and in similar business areas.

EFFECTS OF FEDERAL FUNDING FOR DEFENSE PROGRAMS

The Company continues to have over 85% of its contracts with the Department of
Defense. Although the Defense budget has not yet been authorized for GFY98, the
Company does not project any significant reductions in the funding on any of its
major programs. Further, the results of the Quadrennial Defense Review (QDR)
would appear to be positive for the Company's long-term business prospects.
However, such projections are always subject to the impact of unanticipated
events in the international arena on the defense budget priorities of the United
States.



<PAGE>   10



                                    SIGNATURE


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



                                            SPARTA, INC.

                                            /s/ B. WARREN KNUDSON
                                            -----------------------------------
Date:  November 12, 1997                    B. Warren Knudson
                                            Vice President and Chief
                                            Financial Officer
                                            (Principal financial and chief
                                            accounting officer)

<PAGE>   11




                                  EXHIBIT INDEX

                                  SPARTA, INC.

                        QUARTER ENDED SEPTEMBER 30, 1997




<TABLE>
<CAPTION>
Exhibit                                                                   Sequential
  No.                Description of Exhibits                               Page No.
-------              -----------------------                              ----------

<S>                  <C>                                                  <C>   
   11                Statement re: Computation of Per Share Earnings

   27                Financial Data Schedule
</TABLE>