<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        MARCH 31, 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)

                                 (313) 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 Sheet, March 31, 1998 ...................................1

          Statement of Operations for the three month periods
          ended March 31, 1998 and 1997....................................2

          Statement of Changes in Partners' Capital for the three month 
          period ended March 31, 1998 .....................................3

          Statement of Cash Flows for the three month periods
          ended March 31, 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 SHEET
                                 March 31, 1998
                                 (Unaudited)

<TABLE>
<CAPTION>

                                     ASSETS

<S>                                                            <C>         
Cash and cash equivalents                                      $    834,623
Investment in property under leases:
   Operating leases, net                                         13,821,949
   Financing leases, net                                          1,704,853
   Impaired financing lease, net                                     50,000
Accounts receivable                                                     689
Unbilled rent                                                       422,882
Due from related parties                                             27,864
                                                               ------------
Total assets                                                   $ 16,862,860
                                                               ============


                         LIABILITIES & PARTNERS' CAPITAL

Liabilities:
   Accounts payable                                            $     49,724
   Due to related parties                                            29,970
   Security deposits held on leases                                  59,329
                                                               ------------
Total liabilities                                                   139,023
                                                               ------------
Partners' Capital:
Limited partners' capital accounts                               16,687,307
General partners' capital accounts                                   36,530
                                                               ------------  
Total partners' capital                                          16,723,837
                                                               ------------  
Total liabilities & partners' capital                          $ 16,862,860
                                                               ============
</TABLE>



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



                                       1


<PAGE>   4


                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                             STATEMENT OF OPERATIONS
               for the three months ended March 31, 1998 and 1997
                                 (Unaudited)

<TABLE>
<CAPTION>
                                                        1998         1997
                                                        ----         ----
<S>                                                   <C>          <C>      
Operating revenue:
   Rental income                                      $ 427,770    $ 393,115
   Finance income                                        59,216       84,492
                                                      ---------    ---------
                Total operating revenue                 486,986      477,607
                                                      ---------    ---------
Operating costs and expenses:
   Depreciation                                          54,700       48,831
   General and administrative                            29,317       45,509
                                                      ---------    ---------
                Total operating costs and expenses       84,017       94,340
                                                      ---------    ---------
                Income from operations                  402,969      383,267
                                                      ---------    ---------
Other income:
   Gain on sale of equipment                              4,713       
   Interest income (expense)                                156       28,670
   Other                                                  1,019          231
                                                      ---------    ---------
                Total other income                        5,888       28,901
                                                      ---------    ---------
Net income                                              408,857      412,168

Net income allocable to general partners                  4,089        4,122
                                                      ---------    ---------
Net income allocable to limited partners              $ 404,768    $ 408,046
                                                      =========    =========
Net income per limited partnership unit               $   20.28    $   21.29
                                                      =========    =========
Weighted average number of limited partnership
   units outstanding                                     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 three months ended March 31, 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 - ($27.13 per unit)                     (541,693)           -        (541,693)

Net income                                             404,768        4,089         408,857
                                      -------     ------------     --------    ------------
Balance, March 31, 1998               19,963      $ 16,687,307     $ 36,530    $ 16,723,837
                                      =======     ============     ========    ============
</TABLE>




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

                                       3



<PAGE>   6
                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                             STATEMENT OF CASH FLOWS
               for the three months ended March 31, 1998 and 1997
                                 (Unaudited)

<TABLE>
<CAPTION>
                                                           1998         1997
                                                           ----         ----
<S>                                                     <C>          <C>      
Cash flows from operating activities:
   Net Income                                           $ 408,857    $ 412,168
   Adjustments to net income:
        Depreciation                                       54,700       48,831
        Gain on sale of equipment                          (4,713)           -
        Increase in unbilled rent                         (11,771)      (7,167)
        Decrease in receivables                            10,825        1,761
        (Decrease) increase in payables                    31,693      (31,238)
        Decrease in security deposits held on leases           -        (6,624)
                                                        ---------    ---------
Net cash provided by operating activities                 489,591      417,731
                                                        ---------    ---------
Cash flows from investing activities:
   Purchase and construction advances of real estate
        for operating leases                                    -     (376,890)
   Reduction of net investment in financing leases        362,831      104,183
                                                        ---------    ---------
Net cash provided by (used in) investing activities       362,831     (272,707)
                                                        ---------    ---------
Cash flows from financing activities:
   (Increase) decrease in due from related parties           (373)       9,899
   (Decrease) increase in due to related parties          (29,413)      24,922
   Distributions to limited partners                     (541,693)    (502,683)
                                                        ---------    ---------
Net cash provided by (used in) financing activities      (571,479)    (467,862)
                                                        ---------    ---------

Net decrease  in cash and cash equivalents                280,943     (322,838)

Cash and cash equivalents, beginning of period            553,680      690,175
                                                        ---------    ---------
Cash and cash equivalents, end of period                $ 834,623    $ 367,337
                                                        =========    =========
</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 March 31, 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 March 31, 1998 and the
       statements of operations and cash flows for the period ending March 31,
       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 March 31, 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                       (412,808)
                                                          -------------
           Total                                          $  13,821,949
                                                          =============
</TABLE>


3.     NET INVESTMENT IN FINANCING LEASES:

       The net investment in financing leases as of March 31, 1998 is 
       comprised of the following:

<TABLE>
<S>                                                       <C>          
           Minimum lease payments to be received          $   1,955,229
           Estimated residual value                             213,036
                                                          -------------
           Gross investment in financing leases               2,168,265
           Less unearned income                                (463,412)
                                                          -------------  
           Net investment in financing leases             $   1,704,853
                                                          =============
</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 Partnership does not have a financing commitment for
this leverage.

         At March 31, 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 March 31, 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:

         For the three month periods ended March 31, 1998 and 1997 the
Partnership earned operating revenues totaling approximately $487,000 and
$478,000 respectively.

         For the three months ended March 31, 1998, the Partnership incurred
expenses totaling approximately $84,000, comprised of general and administrative
expenses and depreciation, as compared to $94,000 for the three months ending
March 31, 1997.

         In February,  1998, Cypress Partners 1995, Ltd. exercised a purchase  
option on their equipment  lease. The Partnership recognized a gain of $4,700 
on this transaction.

         As a result of the above the Partnership earned net income of
approximately $409,000 for the three months ended March 31, 1998. Based upon the
results of operations for the three months ended March 31, 1998, the Partnership
announced distributions totaling $540,000, of which $471,935 was distributed to
its limited partners on April 15, 1998 and the remaining $68,065 was
distributed to those limited partners who elected to receive distributions on a
monthly basis on February 15, 1998 and March 15, 1998.





                                       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:  May 15, 1998






                                       10
<PAGE>   13
                                 Exhibit Index
                                 -------------


<TABLE>
<CAPTION>

Exhibit No.                   Description
-----------                   -----------
<S>                           <C>    
    27                        Financial Data Schedule

</TABLE>