<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             SEPTEMBER 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

<TABLE>
<CAPTION>
PART I     FINANCIAL INFORMATION                                                          Page

<S>                                                                                        <C>
Item 1.    Balance Sheets, September 30, 1998 and December 31, 1997.........................1

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

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

           Statements of Cash Flows for the nine month periods
           ended September 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
</TABLE>


                                       i

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

<TABLE>
<CAPTION>

                                                                        SEPTEMBER 30,     DECEMBER 31,
                                                                            1998             1997
                                                                         -----------      -----------
                                                                         (Unaudited)
                                                ASSETS
<S>                                                                      <C>              <C>
Cash and cash equivalents                                                $   512,505      $   553,680
Investment in property under leases:
   Operating leases, net                                                  13,712,549       13,876,649
   Financing leases, net                                                   1,496,427        2,062,971
   Impaired financing lease, net                                              50,000           50,000
Accounts receivable                                                              153           11,514
Unbilled rent                                                                537,176          411,111
Due from related parties                                                     327,846           27,491
                                                                         -----------      -----------

Total assets                                                             $16,636,656      $16,993,416
                                                                         ===========      ===========


                                    LIABILITIES & PARTNERS' CAPITAL

Liabilities:
   Accounts payable                                                      $    12,883      $    18,031
   Due to related parties                                                    103,108           59,383
   Security deposits held on leases                                           59,329           59,329
                                                                         -----------      -----------

Total liabilities                                                            175,320          136,743
                                                                         -----------      -----------

Partners' Capital:
Limited partners' capital accounts                                        16,416,700       16,824,232
General partners' capital accounts                                            44,636           32,441
                                                                         -----------      -----------

Total partners' capital                                                   16,461,336       16,856,673
                                                                         -----------      -----------

Total liabilities & partners' capital                                    $16,636,656      $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                 Nine months ended
                                                              September 30,                     September 30,
                                                       --------------------------       --------------------------

                                                                Unaudited                         Unaudited

                                                          1998            1997             1998            1997
                                                       ----------      ----------       ----------      ----------
<S>                                                    <C>             <C>              <C>             <C>       
Operating revenue:
   Rental income                                       $  427,770      $  404,593       $1,283,310      $1,227,330
   Finance income                                          44,633          83,251          152,473         254,054
                                                       ----------      ----------       ----------      ----------

               Total operating revenue                    472,403         487,844        1,435,783       1,481,384
                                                       ----------      ----------       ----------      ----------

Operating costs and expenses:
   Depreciation                                            54,700          53,772          164,100         154,960
   General and administrative                              15,401          12,655           61,826          75,779
                                                       ----------      ----------       ----------      ----------

               Total operating costs and expenses          70,101          66,427          225,926         230,739
                                                       ----------      ----------       ----------      ----------

               Income from operations                     402,302         421,417        1,209,857       1,250,645
                                                       ----------      ----------       ----------      ----------

Other income (expense):
  Gain on sale of equipment                                    --           9,299            4,713           9,299
   Interest income (expense)                                  102          (2,559)             418          50,302
   Other                                                    3,274           1,851            4,520           2,292
                                                       ----------      ----------       ----------      ----------

               Total other income, net                      3,376           8,591            9,651          61,893
                                                       ----------      ----------       ----------      ----------

Net income                                                405,678         430,008        1,219,508       1,312,538

Net income allocable to general partners                    4,057           4,300           12,195          13,125
                                                       ----------      ----------       ----------      ----------

Net income allocable to limited partners               $  401,621      $  425,708       $1,207,313      $1,299,413
                                                       ==========      ==========       ==========      ==========

Net income per limited partnership unit                $    20.12      $    21.29       $    60.48      $    64.97
                                                       ==========      ==========       ==========      ==========

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 nine months ended September 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 - ($80.89 per unit)                      (1,614,845)             --      (1,614,845)

Net income                                              1,207,313           12,195      1,219,508
                                    -----------       -----------      -----------     ----------

Balance, September 30, 1998              19,963       $16,416,700      $    44,636    $16,461,336
                                    ===========       ===========      ===========    ===========
</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 nine month periods ended September 30, 1998 and 1997
                                   (Unaudited)

<TABLE>
<CAPTION>

                                                                          1998               1997

<S>                                                                   <C>               <C>                  
Cash flows from operating activities:
   Net Income                                                         $ 1,219,508       $ 1,312,538          
   Adjustments to net income:                                      
        Depreciation                                                      164,100           154,960
        Gain on sale of equipment                                          (4,713)           (9,299)
        Increase in unbilled rent                                        (126,065)         (130,624)
        Decrease in receivables                                            11,361             3,013
        Increase (decrease) in payables                                    (5,147)               84
        Increase (decrease) in prepaid rents                                   --           (43,916)
        Security deposits received                                             --            (6,624)
                                                                      -----------       -----------
                                                                   
Net cash provided by operating activities                               1,259,044         1,280,132
                                                                      -----------       -----------
                                                                   
Cash flows from investing activities:                              
   Purchase of real estate for operating leases                                --        (1,865,965)
   Disposition of real estate for operating leases                             --           572,000
   Reduction of construction loan draws                                        --           939,778
   Proceeds from sale of equipment                                                           15,842      
   Reduction of net investment in financing leases                        571,256           498,171
                                                                      -----------       -----------
                                                                   
Net cash provided by (used in) investing activities                       571,256           159,826
                                                                      -----------       -----------
                                                                   
Cash flows from financing activities:                              
   (Increase) decrease in due from related parties                       (300,355)           10,364
   Increase in due to related parties                                      43,725             3,682
   Distributions to limited partners                                   (1,614,845)       (1,596,062)
                                                                      -----------       -----------
                                                                   
Net cash provided by financing activities                              (1,871,475)       (1,582,016)
                                                                      -----------       -----------
                                                                   
Net increase in cash                                                      (41,175)         (142,058)
                                                                   
Cash, beginning of period                                                 553,680           690,175
                                                                      -----------       -----------
                                                                   
Cash, end of period                                                   $   512,505       $   548,117
                                                                      ===========       ===========
</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 upon formation of
       the Partnership were 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 each contributed $100 in
       cash to the Partnership as a capital contribution. 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.

       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 September 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 September 30, 1998 and the
       statements of operations and cash flows for the period ending September
       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.



                                       5


<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 September 30, 1998 is
       comprised of the following:

<TABLE>

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

                                                                    14,234,757
           Less accumulated depreciation                              (522,208)

           Total                                                 $  13,712,549
                                                                 =============
</TABLE>


3.     NET INVESTMENT IN FINANCING LEASES:

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

<TABLE>

<S>                                                             <C>          
           Minimum lease payments to be received                $   1,653,546
           Estimated residual value                                   213,036
                                                                -------------

           Gross investment in financing leases                     1,866,582
           Less unearned income                                      (370,155)

           Net investment in financing leases                   $   1,496,427
                                                                =============
</TABLE>




                                       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 Sponsor is in active negotiations for the financing
commitment for this leverage.

     At September 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 September 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 SEPTEMBER 30, 1998. During the three months ended
September 30, 1998 (the "Quarter") total operating revenue decreased 3% to
$472,000 as compared to $488,000 for the three months ended September 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 $70,000 for the Quarter as compared
to approximately $66,000 for the 1997 Quarter.

     Other income declined to $3,376 in the Quarter from $8,591 in the 1997
Quarter, principally due to the recognition of a gain on sale of equipment in
the 1997 Quarter.

     As a result of the foregoing, the Partnership's net income decreased 6% to
$406,000 for the Quarter as compared to $430,000 for the 1997 Quarter.


     NINE MONTHS ENDED SEPTEMBER 30, 1998. During the nine months ended
September 30, 1998 ("1998") operating revenue decreased 3% to $1,436,000 as
compared to $1,481,000 for the nine months ended September 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 $226,000 for 1998 as compared to
approximately $231,000 for 1997.

     Other income decreased to $9,651 in 1998 from approximately $62,000 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 7% to
$1,220,000 for 1998 as compared to $1,313,000 for 1997.


     DISTRIBUTIONS. The Partnership announced third quarter distributions of
$517,000, of which $447,782 was distributed to its limited partners on October
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:  November 13, 1998
                           




                                       10
<PAGE>   13

                               INDEX TO EXHIBITS


           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