<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, 1999                       
                               -------------------------------------------------
                                       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>                                                                                   <C>
Item 1.           Balance Sheets, March 31, 1999 and December 31, 1998...................................1

                  Statements of Operations for the three months
                  ended March 31, 1999 and 1998..........................................................2

                  Statement of Changes in Partners' Capital for the three months
                  ended March 31, 1999 ..................................................................3

                  Statements of Cash Flows for the three months
                  ended March 31, 1999 and 1998..........................................................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..............................................................................................11
</TABLE>


                                       i

<PAGE>   3

                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                                  BALANCE SHEET


<TABLE>
<CAPTION>

                                                           (Unaudited)
                                                             MARCH 31,   DECEMBER 31,
                                                               1999           1998
                                     ASSETS

<S>                                                        <C>           <C>        
Cash and cash equivalents                                  $   575,878   $   493,136
Restricted cash                                                 86,884       153,142
Investment in property under leases:
   Operating leases, net                                    19,682,829    19,340,098
   Financing leases, net                                     2,576,521     1,249,313
   Impaired financing leases, net                               56,866        50,000
Accounts receivable                                            251,378       154,948
Unbilled rent, net                                             613,887       571,705
Due from related parties                                       126,279       140,948
Deferred financing costs, net                                  441,446       390,066
                                                           -----------   -----------

    Total assets                                           $24,411,968   $22,543,356
                                                           ===========   ===========


                         LIABILITIES & PARTNERS' CAPITAL

Liabilities:
   Accounts payable and accrued expenses                   $   123,020   $   165,907
   Due to related parties                                       79,262        36,662
   Notes Payable                                             8,194,000     6,200,000
   Security deposits held on leases                             59,329        59,329
                                                           -----------   -----------

    Total liabilities                                        8,455,611     6,461,898
                                                           -----------   -----------

Partners' Capital:
Limited partners' capital accounts                          15,906,982    16,035,439
General partners' capital accounts                              49,375        46,019
                                                           -----------   -----------

    Total partners' capital                                 15,956,357    16,081,458
                                                           -----------   -----------

    Total liabilities & partners' capital                  $24,411,968   $22,543,356
                                                           ===========   ===========
</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, 1999 and 1998
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                       1999       1998
<S>                                                  <C>        <C>     
Operating revenue:
   Rental income                                     $543,189   $427,770
   Finance income                                      16,200     59,216
                                                     --------   --------

                Total operating revenue               559,389    486,986
                                                     --------   --------

Operating costs and expenses:
   Depreciation                                        68,908     54,700
   General and administrative                          17,534     29,317
   Amortization of debt issuance costs                 11,319       --
   Interest Expense                                   130,677       --
                                                     --------   --------

                Total operating costs and expenses    228,438     84,017
                                                     --------   --------

                Income from operations                330,951    402,969
                                                     --------   --------

Other income:
   Interest income                                      1,902        156
   Gain on sale of equipment                             --        4,713
   Other                                                2,739      1,019
                                                     --------   --------

                Total other income                      4,641      5,888
                                                     --------   --------

Net income                                            335,592    408,857

Net income allocable to general partner                 3,356      4,089
                                                     --------   --------

Net income allocable to limited partners             $332,236   $404,768
                                                     ========   ========

Net income per limited partnership unit              $  16.64   $  20.28
                                                     ========   ========

Weighted average number of limited partnership
   units outstanding                                   19,963     19,963
                                                     ========   ========
</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, 1999
                                   (Unaudited)

<TABLE>
<CAPTION>

                                         Limited      Limited         General        Total
                                        Partners'     Partners'       Partners'    Partners'
                                          Units       Accounts        Accounts      Capital
<S>                                 <C>            <C>             <C>            <C>
Balance, December 31, 1998                19,963     16,035,439          46,019     16,081,458


Distributions - ($23.08 per unit)           --         (460,693)           --         (460,693)

Net income                                  --          332,236           3,356        335,592
                                    ------------   ------------    ------------   ------------

Balance, March 31, 1999                   19,963   $ 15,906,982    $     49,375   $ 15,956,357
                                    ============   ============    ============   ============
</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, 1999 and 1998
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                           1999           1998
<S>                                                                    <C>            <C>        
Cash flows from operating activities:
   Net Income                                                          $   335,592    $   408,857
   Adjustments to net income:
        Depreciation                                                        68,908         54,700
        Amortization of debt issuance costs                                 11,319           --
        Gain on sale of equipment                                             --           (4,713)
        (Increase) in unbilled rent                                        (42,182)       (11,771)
        (Increase) decrease in accounts receivable                         (96,430)        10,825
        Increase (decrease) in accounts payable and accrued expenses       (42,888)        31,693
                                                                       -----------    -----------

Net cash provided by operating activities                                  234,319        489,591
                                                                       -----------    -----------

Cash flows from investing activities:
   Purchase and construction advances of real estate
        for operating leases                                              (411,639)          --
   Purchase of equipment for financing leases                           (1,459,099)          --
   Principal payments on financing leases                                  125,026        362,831
                                                                       -----------    -----------

Net cash used in investing activities                                   (1,745,712)       362,831
                                                                       -----------    -----------

Cash flows from financing activities:
   Decrease (increase) in due from related parties                          14,669           (373)
   Increase (decrease) in due to related parties                            42,600        (29,413)
   Proceeds from issuance of notes payable                               1,994,000           --
   Debt issuance costs                                                     (62,699)          --
   Issuance of limited partnership units                                      --             --
   Offering costs                                                             --             --
   Distributions to limited partners                                      (460,693)      (541,693)
   Decrease in restricted cash                                              66,258           --
                                                                       -----------    -----------

Net cash provided by financing activities                                1,594,135       (571,479)
                                                                       -----------    -----------

Net (decrease) increase in cash and cash equivalents                        82,742        280,943

Cash and cash equivalents, beginning of period                             493,136        553,680
                                                                       -----------    -----------

Cash and cash equivalents, end of period                               $   575,878    $   834,623
                                                                       ===========    ===========
</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. 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 March 31, 1999, 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.

       The balance sheet of the Partnership as of March 31, 1999 and the
       statements of operations and cash flows for the period ending March 31,
       1999 and 1998 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, 1999 is comprised
of the following:

<TABLE>

<S>                                          <C>         
          Land                               $  8,126,891
          Building and improvements            11,662,240
          Construction draws on properties        548,639
                                             ------------
          
                                               20,337,770
          Less accumulated depreciation          (654,941)
                                             ------------
          Total                              $ 19,682,829
                                             ============
</TABLE>

3.     NET INVESTMENT IN FINANCING LEASES:

       The net investment in financing leases as of March 31, 1999 is comprised
of the following:

<TABLE>

<S>                                               <C>        
          Minimum lease payments to be received   $ 3,075,764
          Estimated residual value                    193,101
                                                  -----------

          Gross investment in financing leases      3,268,865
                                                  -----------
          Less unearned income                       (692,344)
                                                  -----------
          Net investment in financing leases      $ 2,576,521
                                                  ===========
</TABLE>

4.     NOTES PAYABLE:

       In November, 1998, the Partnership entered into a $6.2 million term note,
       the proceeds of which were used to acquire additional properties. The
       note has a 10 year term, is collaterized by certain properties subject to
       operating leases, and bears an interest rate of 8.37% per annum.

       In March, 1999, the Partnership entered into an additional $2.0 million
       term note. The note also has a 10 year term, is collaterized by certain
       properties subject to operating leases, and bears an interest rate of
       8.5% per annum.

       Debt issuance costs of approximately $453,000 in aggregate were incurred
       in connection with the issuance of the notes, and will be amortized using
       the straight-line method to interest expense over the 10 year term.

                                       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.

         In November, 1998 the Partnership entered into a $6.2 million term
note. The Partnership entered into an additional $1.994 million term note in
March, 1999. Proceeds from the notes were used to acquire additional properties.
The notes have a 10 year term, are collaterized by certain properties subject to
operating leases, and bear interest at rates ranging from 8.37 to 8.5% per
annum.

         During the three months ended March 31, 1999, the Partnership funded
$401,639, including acquisition fees, for two real estate properties under
construction. One of the construction properties was completed in March, 1999 at
a total cost of $1,338,750. At March 31, 1999, the unfunded commitment on the
remaining property under construction was $1.1 million. The Partnership also
purchased four equipment leases in the quarter for $1,459,100, including
acquisition fees.

                                       7
<PAGE>   10

                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                         PART I - FINANCIAL INFORMATION



         At March 31, 1999, the partnership had a portfolio of 16 properties
located in 10 states, with a cost of $20.3 million, including one property under
construction, and ten performing equipment leases with an original investment of
$3.7 million. As of March 31, 1999 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 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 MARCH 31, 1999. During the three months ended March
31, 1999 (the "Quarter") total operating revenue increased 15% to $559,000 as
compared to $487,000 for the three months ended March 31, 1998 (the "1998
Quarter"). The increase in revenues resulted from the acquisition of additional
properties in December, 1998, offset by the impairment of two equipment
financing leases.

         General and administrative expenses were approximately $69,000 for the
Quarter as compared to approximately $55,000 for the 1998 Quarter.

         Interest expense in the amount of $131,000 and amortization expense of
$11,000 were incurred during the Quarter related to the notes payable issuance.
Other income declined to $4,641 in the Quarter from $5,888 in the 1998 Quarter.

         As a result of the foregoing, the Partnership's net income decreased
18% to $336,000 for the Quarter as compared to $409,000 for the 1998 Quarter.

         DISTRIBUTIONS. The Partnership announced first quarter distributions of
$500,000, of which $432,000 was distributed to its limited partners on April 16,
1999 and the remaining $68,000 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

                                       9
<PAGE>   12

                   CAPTEC FRANCHISE CAPITAL PARTNERS L.P. III
                           PART II - OTHER INFORMATION

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)

           4.1             Amended Agreement of Limited Partnership of
                           Registrant. (Incorporated by reference to the
                           corresponding exhibit in the Registrant's Form 10-K
                           for the year ended December 31, 1998)

           10.1            Promissory Note dated November 28, 1998 between
                           Registrant and National Realty Funding L.C.
                           (Incorporated by reference to the corresponding
                           exhibit in the Registrant's Form 10-K for the year
                           ended December 31, 1998)

           10.2            Promissory Note dated March 30, 1999 between 
                           Registrant and National Realty Funding L.C.

           27              Financial Data Schedule

           99.1            Pages 12-16 of the final Prospectus dated August 12,
                           1994, as supplemented. (Incorporated by reference
                           from the final Prospectus filed with the Securities
                           and Exchange Commission pursuant to Rule 424 (b)
                           promulgated under the Securities Act of 1933, as
                           amended. S.E.C. File No. 33-77510C)

           (b) Reports on Form 8-K:

           There were no reports filed on Form 8-K for the first quarter ended
March 31, 1999.

                                       10
<PAGE>   13

                                   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 Net Lease Realty, Inc.
                                      Managing General Partner of
                                      Captec Franchise Capital Partners L.P. III



                              By:      /s/  W. Ross Martin
                                       -----------------------------------------
                                       W. Ross Martin
                                       Executive Vice President,
                                       Chief Financial Officer

                              Date:    May 14, 1999

                                       11
<PAGE>   14

                                 EXHIBIT INDEX



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)

4.1       Amended Agreement of Limited Partnership of Registrant. (Incorporated
          by reference to the corresponding exhibit in the Registrant's Form
          10-K for the year ended December 31, 1998)

10.1      Promissory Note dated November 28, 1998 between Registrant and
          National Realty Funding L.C. (Incorporated by reference to the
          corresponding exhibit in the Registrant's Form 10-K for the year 
          ended December 31, 1998)

10.2      Promissory Note dated March 30, 1999 between Registrant and National 
          Realty Funding L.C.

27        Financial Data Schedule

99.1      Pages 12-16 of the final Prospectus dated August 12, 1994, as
          supplemented. (Incorporated by reference from the final Prospectus
          filed with the Securities and Exchange Commission pursuant to Rule
          424(b) promulgated under the Securities Act of 1933, as amended.
          S.E.C. File No. 33-77510C)