<PAGE>   1
                    U.S. SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  FORM 10-QSB


(Mark One)
  [X]           QUARTERLY REPORT UNDER SECTION 13 OR 15(D) OF THE
                        SECURITIES EXCHANGE ACT OF 1934


FOR THE QUARTERLY PERIOD ENDED          JUNE 30, 1998
                                ------------------------------------------------
                                             OR

  [ ]           TRANSITION REPORT UNDER SECTION 13 OR 15 (D) OF THE
                        EXCHANGE ACT

FOR THE TRANSITION PERIOD FROM                  TO
                                ----------------  ------------------------------

COMMISSION FILE NUMBER:     33-77510-C
                        --------------------------------------------------------

                 Captec Franchise Capital Partners L.P. III
--------------------------------------------------------------------------------
           (Exact name of registrant as specified in its charter)


    Delaware                                            38-3160141
--------------------------------------------------------------------------------
    (State or other jurisdiction                        (IRS Employer
    of incorporation or organization)                   Identification Number)


               24 Frank Lloyd Wright Drive, Lobby L, 4th Floor
                P.O. Box 544, Ann Arbor, Michigan  48106-0544
--------------------------------------------------------------------------------
                    (Address of principal executive offices)


                               (734) 994-5505
--------------------------------------------------------------------------------
                         (Issuer's telephone number)

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

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 of
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
filing requirements for the past 90 days.
Yes     X       No
     ------        ------

              APPLICABLE ONLY TO ISSUERS INVOLVED IN BANKRUPTCY
                 PROCEEDINGS DURING THE PRECEDING FIVE YEARS

Check whether the registrant filed all documents and reports required to be
filed by Section 12, 13 or 15(d) of the Exchange Act after the distribution of
securities under a plan confirmed by court.  Not Applicable.

                      APPLICABLE ONLY TO CORPORATE ISSUERS

State the number of shares outstanding of each of the issuer's classes of
common equity, as of the latest practicable date:  Not Applicable

Transitional Small Business Disclosure Format (check one)  Yes        No  x
                                                               -----    -----

<PAGE>   2




                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III

                              INDEX TO FORM 10-QSB




PART I   FINANCIAL INFORMATION                                           Page


Item 1.  Balance Sheets, June 30, 1998 and December 31, 1997 ...........   1

         Statements of Operations for the three and six month periods
             ended June 30, 1998 and 1997 ..............................   2

         Statement of Changes in Partners' Capital for the six month 
             period ended June 30, 1998 ................................   3

         Statements of Cash Flows for the six month periods
             ended June 30, 1998 and 1997 ..............................   4

         Notes to Financial Statements .................................   5

Item 2.  Management's Discussion and Analysis of Financial Condition
         and Results of Operations  ....................................   7


PART II  OTHER INFORMATION..............................................   9


SIGNATURES..............................................................  10 



                                       i


<PAGE>   3
                  CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                                BALANCE SHEETS

<TABLE>
<CAPTION>

                                                                       JUNE 30,           DECEMBER 31,
                                                                         1998                1997
                                                                    ----------------   ------------------
                                                                      (Unaudited)
                                                 ASSETS
<S>                                                                    <C>                  <C>      
Cash and cash equivalents                                              $    752,101         $    553,680
Investment in property under leases:
   Operating leases, net                                                 13,767,249           13,876,649
   Financing leases, net                                                  1,604,855            2,062,971
   Impaired financing lease, net                                             50,000               50,000
Accounts receivable                                                             206               11,514
Unbilled rent                                                               498,398              411,111
Due from related parties                                                     82,432               27,491
                                                                       ------------         ------------
Total assets                                                           $ 16,755,241         $ 16,993,416
                                                                       ============         ============

                                    LIABILITIES & PARTNERS' CAPITAL

Liabilities:
   Accounts payable                                                    $     43,057         $     18,031
   Due to related parties                                                    65,196               59,383
   Security deposits held on leases                                          59,329               59,329
                                                                       ------------         ------------
Total liabilities                                                           167,582              136,743
                                                                       ------------         ------------
Partners' Capital:
Limited partners' capital accounts                                       16,547,080           16,824,232
General partners' capital accounts                                           40,579               32,441
                                                                       ------------         ------------
Total partners' capital                                                  16,587,659           16,856,673
                                                                       ------------         ------------
Total liabilities & partners' capital                                  $ 16,755,241         $ 16,993,416
                                                                       ============         ============
</TABLE>


The accompanying notes are an integral part of the financial statements.



                                      1



<PAGE>   4
                  CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                           STATEMENTS OF OPERATIONS


<TABLE>
<CAPTION>
                                                               Three months ended                    Six months ended
                                                                   June 30,                               June 30,
                                                          --------------------------            -------------------------
                                                                  Unaudited                              Unaudited        
                                                             1998            1997                 1998              1997    
                                                             ----            ----                 ---               ----    
<S>                                                       <C>             <C>                  <C>               <C>        
Operating revenue:                                                                                                          
   Rental income                                          $ 427,770       $ 429,622            $ 855,540         $ 822,737  
   Finance income                                            48,624          86,311              107,840           170,803  
                                                          ---------       ---------            ---------         ---------  
               Total operating revenue                      476,394         515,933              963,380           993,540  
                                                          ---------       ---------            ---------         ---------  
Operating costs and expenses:                                                                                               
   Depreciation                                              54,700          52,357              109,400           101,188  
   General and administrative                                17,108          17,615               46,424            63,124  
                                                          ---------       ---------            ---------         ---------  
               Total operating costs and expenses            71,808          69,972              155,824           164,312  
                                                          ---------       ---------            ---------         ---------  
               Income from operations                       404,586         445,961              807,556           829,228  
                                                          ---------       ---------            ---------         ---------  
Other income (expense):                                                                                                     
  Gain on sale of equipment                                       -               -                4,713                 -  
   Interest income                                              160          24,272                  316            52,861  
   Other                                                        228             128                1,247               440  
                                                          ---------       ---------            ---------         ---------  
               Total other income, net                          388          24,400                6,276            53,301  
                                                          ---------       ---------            ---------         ---------  
Net income                                                  404,974         470,361              813,832           882,529  
                                                                                                                            
Net income allocable to general partners                      4,050           4,704                8,138             8,825  
                                                          ---------       ---------            ---------         ---------  
Net income allocable to limited partners                  $ 400,924       $ 465,657            $ 805,694         $ 873,704  
                                                          =========       =========            ==========        =========  
Net income per limited partnership unit                   $   20.08       $   23.28            $   40.36         $   43.69  
                                                          =========       =========            =========         =========
Weighted average number of limited partnership                                                                              
   units outstanding                                         19,963          20,000               19,963            20,000  
                                                          =========       =========            =========         =========  
</TABLE>           
                   
      
      
The accompanying notes are an integral part of the financial statements.



                                      2

<PAGE>   5
                  CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                  STATEMENT OF CHANGES IN PARTNERS' CAPITAL
                    for the six months ended June 30, 1998
                                 (Unaudited)

<TABLE>
<CAPTION>

                                           Limited         Limited          General            Total
                                           Partners'       Partners'        Partners'         Partners'
                                            Units          Accounts         Accounts           Capital
                                            -----          --------         --------           -------  
<S>                                           <C>       <C>                <C>              <C>       
Balance, January 1, 1998                      19,963      16,824,232          32,441          16,856,673


Distributions - ($54.24 per unit)                         (1,082,846)              -          (1,082,846)

Net income                                                   805,694           8,138             813,832
                                          ----------    ------------       ---------        ------------
Balance, June 30, 1998                        19,963    $ 16,547,080       $  40,579        $ 16,587,659
                                          ==========    ============       =========        ============
</TABLE>


The accompanying notes are an integral part of the financial statements.



                                      3

<PAGE>   6
                  CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                           STATEMENTS OF CASH FLOWS
            for the six month periods ended June 30, 1998 and 1997
                                 (Unaudited)

<TABLE>
<CAPTION>

                                                                             1998                1997
<S>                                                                       <C>                  <C>      
Cash flows from operating activities:
   Net Income                                                            $  813,832           $  882,529
   Adjustments to net income:
        Depreciation                                                        109,400              101,188
        Gain on sale of equipment                                            (4,713)                   -
        Increase in unbilled rent                                           (87,287)             (83,711)
        Decrease in receivables                                              11,308                1,845
        Increase (decrease) in payables                                      25,026              (42,887)
        Security deposits received                                               -                (6,624)
                                                                         ----------           ----------
Net cash provided by operating activities                                   867,566              852,340
                                                                         ----------           ----------
Cash flows from investing activities:
   Purchase of real estate for operating leases                                   -           (1,865,965)
   Reduction of construction loan draws                                           -              939,778
   Reduction of net investment in financing leases                          462,828              207,851
                                                                         ----------           ----------
Net cash used in investing activities                                       462,828             (718,336)
                                                                         ----------           ----------
Cash flows from financing activities:
   (Increase) decrease in due from related parties                          (54,941)              10,400
   Increase in due to related parties                                         5,814              463,183
   Distributions to limited partners                                     (1,082,846)          (1,044,909)
                                                                         ----------           ----------
Net cash provided by (used in) investing activities                      (1,131,973)            (571,326)
                                                                         ----------           ----------
Net increase in cash                                                        198,421             (437,322)

Cash, beginning of period                                                   553,680              690,175
                                                                         ----------           ----------
Cash, end of period                                                      $  752,101           $  252,853
                                                                         ==========           ==========

</TABLE>


The accompanying notes are an integral part of the financial statements.



                                      4





<PAGE>   7
                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                         NOTES TO FINANCIAL STATEMENTS


1.  THE PARTNERSHIP AND ITS SIGNIFICANT ACCOUNTING PRINCIPLES:

    Captec Franchise Capital Partners L.P. III (the "Partnership"), a Delaware
    limited partnership, was formed on February 18, 1994 for the purpose of
    acquiring income-producing commercial real properties and equipment leased
    on a "triple net" or "double net" basis, primarily to operators of national
    and regional chain and nationally franchised fast food and family style
    restaurants, as well as other national and regional retail chains.  The
    general partners of the Partnership are Captec Franchise Capital
    Corporation III (the "Corporation"), a wholly owned subsidiary of Captec
    Financial Group, Inc. ("Captec"), and Patrick L. Beach, an individual,
    hereinafter collectively referred to as the Sponsor.  Patrick L. Beach is
    also the Chairman of the Board of Directors, President and Chief Executive
    Officer of the Corporation and Captec.  The general partners have each
    contributed $100 in cash to the Partnership as a capital contribution.

    The Partnership commenced a public offering of 20,000 limited partnership
    interests ("Units") on August 12, 1994 and reached final funding in
    August,1996.  Net proceeds after offering expenses were approximately $17.4
    million.  During 1997, the Partnership repurchased a total of 37 units.  At
    June 30, 1998, the Partnership had 19,963 units issued and outstanding.

    Allocation of profits, losses and cash distributions from operations and
    cash distributions from sale or refinancing are made pursuant to the terms
    of the Partnership Agreement.  Profits and losses from operations are
    allocated among the limited partners based upon the number of Units owned.
    In no event will the General Partners be allocated less than one percent of
    profits and losses in any year.

    The balance sheet of the Partnership as of June 30, 1998 and the statements
    of operations and cash flows for the period ending June 30, 1998 and 1997
    have not been audited.  In the opinion of the Management, these unaudited
    financial statements contain all adjustments necessary to present fairly
    the financial position and results of operations and cash flows of the
    Partnership for the periods then ended.  Results of operations for the
    interim periods are not necessarily indicative of results for the full
    year.





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<PAGE>   8

                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III

                         NOTES TO FINANCIAL STATEMENTS



2.  LAND AND BUILDING SUBJECT TO OPERATING LEASES:

    The net investment in operating leases as of June 30, 1998 is comprised of
    the following:


<TABLE>
<CAPTION>
                  <S>                            <C>
                  Land                           $ 5,482,775
                  Building and improvements        8,751,982
                                                 -----------

                                                  14,234,757
                  Less accumulated depreciation     (467,508)
                                                 -----------

                  Total                          $13,767,249
                                                 ===========
</TABLE>



3.  NET INVESTMENT IN FINANCING LEASES:

    The net investment in financing leases as of June 30, 1998 is comprised of
    the following:


<TABLE>
<CAPTION>
               <S>                                    <C>
               Minimum lease payments to be received  $1,806,607
               Estimated residual value                  213,036
                                                      ----------

               Gross investment in financing leases    2,019,643
               Less unearned income                     (414,788)
                                                      ----------

               Net investment in financing leases     $1,604,855
                                                      ==========
</TABLE>



4.  SUBSEQUENT EVENT:

    In August, 1998 the general partnership interest of the Partnership was
    acquired by Captec Net Lease Realty, Inc., an affiliate of Captec, for
    $1,483,000.



                                      6



<PAGE>   9

                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III


                         PART I - FINANCIAL INFORMATION


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

     When used in this discussion, the words, "intends", "anticipates",
"expects", and similar expressions are intended to identify forward-looking
statements.  Such statements are subject to certain risks and uncertainties
which could cause actual results to differ materially from those projected.
Such risks and uncertainties include the following: (i)  a tenant may default
in making rent payments, (ii) a fire or other casualty may interrupt the cash
flow stream from a property, (iii) the properties may not be able to be leased
at the assumed rental rates, (iv) unexpected expenses may be incurred in the
ownership of the properties, and (v) properties may not be able to be sold at
the presently anticipated prices and times.

     As a result of these and other factors, the Partnership may experience
material fluctuations in future operating results on a quarterly or annual
basis, which could materially and adversely affect its business, financial
condition and operating results.  These forward-looking statements speak only
as of the date hereof.  The Partnership undertakes no obligation to publicly
release the results of any revisions to these forward-looking statements which
may be made to reflect events or circumstances after the date hereof or to
reflect the occurrence of unanticipated events.

LIQUIDITY AND CAPITAL COMMITMENTS:

     The Partnership commenced the offering (the "Offering") of up to 20,000
limited partnership units ("Units") registered under the Securities Act of
1933, as amended, by means of a Registration Statement which was declared
effective by the Securities and Exchange Commission on August 12, 1994.  The
Offering reached final funding on August 12, 1996 with subscriptions for the
entire 20,000 Units and funds totaling $20,000,000.  Net proceeds after
offering expenses were $17,400,000.

     During 1998, the Partnership expects to obtain leverage of up to
approximately $8.5 million.  Such leverage, when incurred, will provide
additional funds to be used by the Partnership to purchase properties and
equipment.  Presently, the Partnership does not have a financing commitment for
this leverage.

     At June 30, 1998, the partnership had $14.2 million invested in eleven net
leased real estate properties and $2.5 million invested in eight equipment
packages.  As of June 30, 1998 the Partnership's investments were allocated
approximately 85% to properties and 15% to equipment.  This allocation is
expected to change as additional properties and equipment are acquired.  The
final asset mix allocation is expected to be at least 75%, but not more than
90% properties and up to 25%, but not less than 10% equipment.

     Once substantially all of the Partnership's funds have been applied as
intended, the Partnership expects to require limited amounts of liquid assets
since the form of lease which it intends to use for its properties and
equipment will require lessees to pay all taxes and assessments, maintenance
and repairs items (except, with respect to double net properties, costs
associated with the maintenance and repair of the exterior walls and roof of
the property) and insurance premiums, including casualty insurance.  The
general partners expect that the

                                       7



<PAGE>   10
                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                         PART I - FINANCIAL INFORMATION



cash flow to be generated by the Partnership's properties and equipment will be
adequate to pay operating expenses and provide distributions to Limited
Partners.


RESULTS OF OPERATIONS:

     THREE MONTHS ENDED JUNE 30, 1998.  During the three months ended June 30,
1998 (the "Quarter") total operating revenue decreased 7% to $477,000 as
compared to $516,000 for the three months ended June 30, 1997 (the "1997
Quarter").  The decrease in revenues resulted from the sale of equipment under
one financing lease in February, 1998 and the suspension of revenue associated
with the impairment of one financing lease.

     Operating expenses were approximately $72,000 for the Quarter as compared
to approximately $70,000 for the 1997 Quarter.

     Other income declined to $388 in the Quarter from $24,400 in the 1997
Quarter as interest income was earned in 1997 from funds raised and not yet
used to acquire properties.

     As a result of the foregoing, the Partnership's net income decreased 14%
to $405,000 for the Quarter as compared to $470,000 for the 1997 Quarter.


     SIX MONTHS ENDED JUNE 30, 1998.  During the six months ended June 30, 1998
("1998") operating revenue decreased 3% to $963,000 as compared to $994,000 for
the six months ended June 30, 1997 ("1997").  The decrease in revenues resulted
from the sale of one equipment property in February, 1998 and the suspension of
revenue associated with the impairment of one financing lease.

     Operating expenses were approximately $156,000 for 1988 as compared to
approximately $164,000 for 1997.

     Other income declined to $6,276 in 1988 from approximately $53,000 in
1997, as interest income was earned in 1997 from funds raised and not yet used
to acquire properties.

     As a result of the foregoing, the Partnership's net income decreased 8% to
$814,000 for 1998 as compared to $883,000 for 1997.


     DISTRIBUTIONS.  The Partnership announced second quarter distributions of
$532,000, of which $462,782 was distributed to its limited partners on July 15,
1998 and the remaining $69,218 will be distributed to those limited partners
who elected to receive distributions on a monthly basis.




                                       8



<PAGE>   11

                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III

                          PART II - OTHER INFORMATION
                   
          
Item 1.   Legal Proceedings
          
          None
          
Item 2.   Changes in Securities
          
          None
          
Item 3.   Defaults Upon Senior Securities
          
          None
          
Item 4.   Submission of Matters to a Vote of Security Holders
          
          None
          
Item 5.   Other Information
          
          None
          
Item 6.   Exhibits and Reports on Form 8-K
          

          (a) The following exhibits are included herein or incorporated by
              reference:

          Number    Exhibit

          4         Agreement of Limited Partnership of Registrant. 
                    (Incorporated by reference from Exhibit B of the final 
                    Prospectus dated August 12, 1994, as supplemented and filed 
                    with the Securities and Exchange Commission, S. E. C. File 
                    No. 33-77510C)

          27        Financial Data Schedule



                                       9



<PAGE>   12
                                   SIGNATURES



     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.


                                By:  Captec Franchise Capital Corporation III
                                     Managing General Partner of
                                     Captec Franchise Capital Partners L.P. III



                                By:  /w/ W. Ross Martin                      
                                     -----------------------------------------
                                     W. Ross Martin
                                     Chief Financial Officer and Vice President,
                                     a duly authorized officer

                                Date:  August 14, 1998
                                       



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