<PAGE>   1
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                   Form 10-Q
                       Quarterly Report Under Section 13
                          or 15 (d) of the Securities
                              Exchange Act of 1934



<TABLE>
<S>                                          <C>
For the Quarter Ended
    March 31, 1999                           Commission File Number  0-21260 
----------------------                       --------------------------------
</TABLE>



                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
             ------------------------------------------------------
             (Exact name of Registrant as specified in its charter)


      Delaware                                             36-3763539
   ----------------                                ---------------------------
   State or other                                  IRS Employer Identification
   jurisdiction of                                            Number
   incorporation or
   organization

1300 E. Woodfield Road, Suite 312                  Schaumburg, Illinois 60173
---------------------------------                  --------------------------
     Address of principal                             City, State, Zip Code
      executive offices

Registrant's telephone number:                           (847) 240-6200
                                                         --------------


         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 such filing requirements for the past 90
         days.

                                  (1)  Yes  X   No     
                                           ---      ---

                                  (2)  Yes  X   No     
                                           ---      ---

<PAGE>   2
                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.

                                   FORM 10-Q

                      FOR THE QUARTER ENDED MARCH 31, 1999

<TABLE>
<S>                                                                        <C>
PART I - FINANCIAL INFORMATION

Item 1.

  Index to Financial Statements

    Balance Sheets

      March 31, 1999 (unaudited)                                             3

      December 31, 1998                                                      4

    Statements of Revenue and Expenses (unaudited)

      For the three months ended March 31, 1999                              5

      For the three months ended March 31, 1998                              6

    Statements of Changes in Partners' Equity

      For the three months ended March 31, 1999
        (unaudited)                                                          7

    Statements of Cash Flows (unaudited)

      For the three months ended March 31, 1999                              8

      For the three months ended March 31, 1998                              9

    Notes to Financial Statements                                      10 - 11

Item 2.

  Management's Discussion and Analysis of
    Financial Condition and Results of Operations                      12 - 13

PART II - OTHER INFORMATION

Items 1-6.                                                                  14
</TABLE>


                                       2
<PAGE>   3
                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                                 BALANCE SHEETS
                                 March 31, 1999
                                  (Unaudited)


<TABLE>
<CAPTION>
                                    Liquidating  Continuing 
                                      Limited     Limited 
                                     Partners     Partners       Total
                                   ------------  -----------  -----------
<S>                                <C>          <C>         <C>
ASSETS

Cash and cash equivalents            $  221,926   $4,384,700   $4,606,626
Net investment in direct financing
  leases                                   --        334,560      334,560
Residual interest in CRCA                  --           --           --
Diverted and other assets, net            8,172      112,713      120,885
Datronic assets, net                       --           --           --
                                     ----------   ----------   ----------

                                     $  230,098   $4,831,973   $5,062,071
                                     ==========   ==========   ==========

LIABILITIES AND PARTNERS' EQUITY

Accounts payable and accrued
  expenses                           $      109   $    8,719   $    8,828
Lessee rental deposits                     --            111          111
                                     ----------   ----------   ----------

    Total liabilities                       109        8,830        8,939

Total partners' equity                  229,989    4,823,143    5,053,132
                                     ----------   ----------   ----------

                                     $  230,098   $4,831,973   $5,062,071
                                     ==========   ==========   ==========
</TABLE>


                 See accompanying notes to financial statements

                                       3
<PAGE>   4

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                                 BALANCE SHEETS
                               December 31, 1998


<TABLE>
<CAPTION>
                                    Liquidating  Continuing 
                                      Limited     Limited 
                                     Partners     Partners       Total
                                   ------------  -----------  -----------
<S>                                <C>          <C>         <C>
ASSETS

Cash and cash equivalents            $  225,068   $4,315,347   $4,540,415
Judgment receivable, net                  3,405       46,964       50,369
Net investment in direct financing
  leases                                   --        432,232      432,232
Residual interest in CRCA                  --           --           --
Diverted and other assets, net            8,172      112,713      120,885
Datronic assets, net                       --           --           --
                                     ----------   ----------   ----------

                                     $  236,645   $4,907,256   $5,143,901
                                     ==========   ==========   ==========

LIABILITIES AND PARTNERS' EQUITY

Accounts payable and accrued
  expenses                           $      761   $   21,351   $   22,112
Lessee rental deposits                     --            142          142
                                     ----------   ----------   ----------

    Total liabilities                       761       21,493       22,254

Total partners' equity                  235,884    4,885,763    5,121,647
                                     ----------   ----------   ----------

                                     $  236,645   $4,907,256   $5,143,901
                                     ==========   ==========   ==========
</TABLE>


                 See accompanying notes to financial statements

                                       4
<PAGE>   5

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                       STATEMENTS OF REVENUE AND EXPENSES
                   For the three months ended March 31, 1999
                                  (Unaudited)


<TABLE>
<CAPTION>
                                    Liquidating  Continuing 
                                      Limited     Limited 
                                     Partners     Partners       Total
                                   ------------  -----------  -----------
<S>                                <C>          <C>         <C>
Revenue:
  Lease income                       $     170    $  18,898    $  19,068
  Interest income                        2,423       45,166       47,589
                                     ---------    ---------    ---------

                                         2,593       64,064       66,657
                                     ---------    ---------    ---------

Expenses:
  General Partner's expense
    reimbursement                        7,684      126,728      134,412
  Professional fees                        939       21,548       22,487
  Other operating expenses                 141        2,214        2,355
  Credit for lease losses                 (276)     (23,806)     (24,082)
                                     ---------    ---------    ---------

                                         8,488      126,684      135,172
                                     ---------    ---------    ---------

Net loss                             $  (5,895)   $ (62,620)   $ (68,515)
                                     =========    =========    =========

Net loss - General Partner           $     (59)   $    (626)   $    (685)
                                     =========    =========    =========

Net loss - Limited Partners          $  (5,836)   $ (61,994)   $ (67,830)
                                     =========    =========    =========

Net loss per limited
   partnership unit                  $   (1.14)   $   (0.88)
                                     =========    =========

Weighted average number of limited
   partnership units outstanding         5,100       70,396
                                     =========    =========
</TABLE>


                 See accompanying notes to financial statements

                                       5
<PAGE>   6

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                       STATEMENTS OF REVENUE AND EXPENSES
                   For the three months ended March 31, 1998
                                  (Unaudited)


<TABLE>
<CAPTION>
                                    Liquidating  Continuing 
                                      Limited     Limited 
                                     Partners     Partners       Total
                                   ------------  -----------  -----------
<S>                                <C>          <C>         <C>
Revenue:
  Lease income                       $     552    $  42,995    $  43,547
  Interest income                        2,777       42,920       45,697
                                     ---------    ---------    ---------

                                         3,329       85,915       89,244
                                     ---------    ---------    ---------

Expenses:
  General Partner's expense
    reimbursement                        8,922      144,890      153,812
  Professional fees                      6,459       89,729       96,188
  Other operating expenses                 353        5,152        5,505
  Credit for lease losses              (16,971)    (234,074)    (251,045)
                                     ---------    ---------    ---------

                                        (1,237)       5,697        4,460
                                     ---------    ---------    ---------

Net earnings                         $   4,566    $  80,218    $  84,784
                                     =========    =========    =========

Net earnings - General Partner       $      46    $     802    $     848
                                     =========    =========    =========

Net earnings - Limited Partners      $   4,520    $  79,416    $  83,936
                                     =========    =========    =========

Net earnings per limited
   partnership unit                  $    0.89    $    1.13
                                     =========    =========

Weighted average number of limited
   partnership units outstanding         5,100       70,396
                                     =========    =========
</TABLE>


                 See accompanying notes to financial statements

                                       6
<PAGE>   7

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                   STATEMENTS OF CHANGES IN PARTNERS' EQUITY
                                  (Unaudited)


<TABLE>
<CAPTION>
                                              Liquidating     Continuing
                                  General       Limited         Limited       Total
                                 Partner's     Partners'       Partners'     Partners'
                                  Equity        Equity          Equity        Equity
                               ------------  ------------     -----------  ------------ 
<S>                           <C>           <C>             <C>           <C>
Balance, December 31, 1998*   $      --      $   235,884    $ 4,885,763    $ 5,121,647

  Net loss                           (685)        (5,836)       (61,994)       (68,515)
  Allocation of General
    Partner's Equity                  685            (59)          (626)          --
                              -----------    -----------    -----------    -----------

Balance, March 31, 1999       $      --      $   229,989    $ 4,823,143    $ 5,053,132
                              ===========    ===========    ===========    ===========
</TABLE>


*  Balances are net of $16,221 and $292,056 of General Partner's equity
   previously allocated to Liquidating and Continuing Limited Partners' Equity.


                 See accompanying notes to financial statements

                                       7
<PAGE>   8

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                            STATEMENTS OF CASH FLOWS
                   For the three months ended March 31, 1999
                                  (Unaudited)

<TABLE>
<CAPTION>
                                         Liquidating     Continuing
                                           Limited        Limited
                                          Partners        Partners         Total
                                        ------------    ------------    -----------
<S>                                      <C>            <C>           <C>
Cash flows from operating activities:
  Net loss                                $    (5,895)   $   (62,620)   $   (68,515)
  Adjustments to reconcile net earnings
     to net cash used in operating
    activities:
    Credit for lease losses                      (276)       (23,806)       (24,082)
    Changes in assets and liabilities:
      Judgment receivable, net                  3,405         46,964         50,369
      Accounts payable and
        accrued expenses                         (652)       (12,632)       (13,284)
      Lessee rental deposits                     --              (31)           (31)
                                          -----------    -----------    -----------
                                               (3,418)       (52,125)       (55,543)
                                          -----------    -----------    -----------

Cash flows from investing activities:
  Principal collections on leases                 276        121,478        121,754
                                          -----------    -----------    -----------

Net increase (decrease) in cash and
  cash equivalents                             (3,142)        69,353         66,211
Cash and cash equivalents:
  Beginning of year                           225,068      4,315,347      4,540,415
                                          -----------    -----------    -----------
  End of first quarter                    $   221,926    $ 4,384,700    $ 4,606,626
                                          ===========    ===========    ===========
</TABLE>


                 See accompanying notes to financial statements

                                       8

<PAGE>   9
                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                            STATEMENTS OF CASH FLOWS
                   For the three months ended March 31, 1998
                                  (Unaudited)


<TABLE>
<CAPTION>
                                         Liquidating     Continuing
                                           Limited        Limited
                                          Partners        Partners         Total
                                        ------------    ------------    -----------
<S>                                      <C>            <C>           <C>
Cash flows from operating activities:
  Net earnings                           $     4,566    $    80,218    $    84,784
  Adjustments to reconcile net loss
    to net cash used in operating
    activities:
    Credit for lease losses                  (16,971)      (234,074)      (251,045)
    Changes in assets and liabilities:
      Accounts payable and
        accrued expenses                        (133)        (5,229)        (5,362)
      Lessee rental deposits                  (1,469)       (32,070)       (33,539)
                                         -----------    -----------    -----------
                                             (14,007)      (191,155)      (205,162)
                                         -----------    -----------    -----------

Cash flows from investing activities:
  Principal collections on leases             16,971        435,048        452,019
                                         -----------    -----------    -----------


Net increase in cash and
  cash equivalents                             2,964        243,893        246,857
Cash and cash equivalents:
  Beginning of year                          221,305      3,564,194      3,785,499
                                         -----------    -----------    -----------
  End of first quarter                   $   224,269    $ 3,808,087    $ 4,032,356
                                         ===========    ===========    ===========
</TABLE>


                 See accompanying notes to financial statements

                                       9
<PAGE>   10

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                         NOTES TO FINANCIAL STATEMENTS
                                 March 31, 1999
                                  (Unaudited)


NOTE 1 - ORGANIZATION:

Datronic Equipment Income Fund XX, L.P., a Delaware Limited Partnership (the
"Partnership"), was formed on April 30, 1991 for the purpose of acquiring and
leasing both high- and low-technology equipment. The offering of limited
partnership units terminated on May 1, 1992. See Notes 5, 8 and 10 to the
Partnership's financial statements included in the 1998 Form 10-K for a
discussion of the alleged diversion of Partnership assets in 1991 and 1992 and
the subsequent litigation and settlement, change in general partner, new
classes of limited partners established and amendments to the Partnership
Agreement which occurred.

NOTE 2 - BASIS OF FINANCIAL STATEMENTS:

The accompanying financial statements should be read in conjunction with the
Partnership's financial statements included in the 1998 Form 10-K. The
financial information furnished herein is unaudited but in the opinion of
Management includes all adjustments necessary (all of which are normal
recurring adjustments) for a fair presentation of financial condition and
results of operations. See Note 2 to the Partnership's financial statements
included in the 1998 Form 10-K.

NOTE 3 - LIMITED PARTNERSHIP DISTRIBUTIONS:

In early April 1999, the Partnership made a cash distribution to Limited
Partners who were owners of record on December 31, 1998. This distribution
consisted of two components: (i) the net proceeds from the Price Waterhouse and
Weiss & Company legal actions ($15,000 and $202,000 for Liquidating and
Continuing Limited Partners respectively), and (ii) residual cash resulting from
the net cash flows of the Partnership ($94,000 and $2,116,000 for Liquidating
and Continuing Limited Partners respectively). The portion of the distribution
attributable to legal action proceeds was allocated to each Limited Partner
based on the number of units held at the rate of $2.87 per unit. See Note 8 to
the Partnership's financial statements included in the 1998 Form 10-K. Pursuant
to the Partnership Agreement, residual cash was allocated to each Limited
Partner based on their proportionate share of total partners' capital
attributable to their Class.

NOTE 4 - RESIDUAL INTEREST IN CRCA:

Residual interest in CRCA represents the Partnership's fully reserved 35% (65%
for Fund XVIII) interest in the remaining assets of Computer Rental Corp. of
America, Inc. (CRCA). These assets consisted of a $4.2 million subordinated
note receivable from Personal Computer Rental Corporation (PRC) and $136,000 of
cash. See Note 4 to the


                                      10
<PAGE>   11

                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                 NOTES TO THE FINANCIAL STATEMENTS - CONTINUED



financial statements included in the 1998 Form 10-K. In early April, 1999, CRCA
sold the $4.2 million subordinated note to PCR's senior secured creditor for
$250,000. The Partnership's share of these proceeds along with its share of
CRCA's residual cash, after payment of expenses, will be credited to its
provision for lease losses when distributed to the Partnership.


                                      11
<PAGE>   12
PART I

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

The following discussion and analysis of liquidity and capital resources covers
material changes in the Partnership's financial condition from December 31, 1998
through March 31, 1999. The discussion and analysis of results of operations is
for the three month period ended March 31, 1999 as compared to the corresponding
period in 1998. Any capitalized term not defined herein has been defined or
discussed in the Partnership's 1998 Form 10-K.

Liquidity and Capital Resources

During the three months ended March 31, 1999, Partnership assets continued to
be converted to cash in order to pay Partnership operating expenses and to
provide for the ultimate liquidation of the Partnership. During the three
months ended March 31, 1999, Partnership cash and cash equivalents increased by
$66,000 to $4,606,000 at March 31, 1999 from $4,540,000 at December 31, 1998.
This increase is primarily due to cash receipts from collections on leases of
$122,000 partially offset by cash used in operations of $56,000.

In early April 1999, the Partnership made a cash distribution to Limited
Partners who were owners of record on December 31, 1998. This distribution
consisted of two components: (i) the net proceeds from the Price Waterhouse and
Weiss & Company legal actions ($15,000 and $202,000 for Liquidating and
Continuing Limited Partners respectively), and (ii) residual cash resulting from
the net cash flows of the Partnership ($94,000 and $2,116,000 for Liquidating
and Continued Limited Partners respectively). The portion of the distribution
attributable to legal action proceeds was allocated to each Limited Partner
based on the number of units held at the rate of $2.87 per unit. See Note 8 to
the Partnership's financial statements included in the 1998 Form 10-K. Pursuant
to the Partnership Agreement, residual cash was allocated to each Limited
Partner based on their proportionate share of total partners' capital
attributable to their Class.

The Partnership's sources of future liquidity are expected to come from
remaining cash-on-hand after the April 1999 distribution, the cash receipts
from leases owned by the Partnership as well as the disposition of Diverted
Assets (consisting primarily of an office building in Schaumburg, Illinois).
The lease portfolio is scheduled to be fully liquidated by March 2001. The
general partner expects the Diverted Assets to be converted to cash during 1999
thereby enabling the Partnership to pay an additional distribution in early
2000. After all assets are disposed of and the proceeds are distributed to the
limited partners, the Partnership will be required to file final reports with
the Securities and Exchange Commission and the Internal Revenue Service. The
general partner expects this to occur sometime during the year 2001.


                                      12

<PAGE>   13

Results of Operations

The Partnership had a net loss of $69,000 for the three month period ended
March 31, 1999, in the aggregate for all classes of partners. This compares to
net earnings of $85,000 for the same period in 1998. Differences in operating
results between Liquidating and Continuing Limited Partners are attributable to
lease income, acquisition costs, and expenses associated with new lease
investments made since the March 4, 1993 Settlement. Liquidating Limited
Partners do not participate in these post Settlement activities. Significant
factors affecting overall operating results for the three month period ended
March 31, 1999 as compared to the corresponding period in 1998 include the
following:

Lease income:

Since January 1997, the Partnership has been in its Liquidating Phase which
prohibits investing in any new leases. Accordingly, the lease portfolio has
continued to decrease as collections are made, resulting in a continued decline
in lease income. This trend will continue as the Partnership liquidates its
remaining leases.

Interest income:

Interest income includes earnings on invested cash balances. Interest income
for 1999 was higher than 1998 because of higher average invested cash balances.

General Partner's expense reimbursement:

General Partner's expense reimbursement includes payments to LRC for expenses
it incurred as general partner in excess of those covered by its partner
distributions. These expenses include expenses incurred by LRC in its
management of the day-to-day operations of the Partnership.

Professional fees:

Professional fees for the three months ended March 31, 1999 reflect a
decreasing level of professional services required as a result of the decrease
in the Partnership's lease portfolio and related activities. Included in the
1998 amount are fees paid in connection with the litigation against the
Partnership's former accountants.

Credit for lease losses:

This credit reflects recovery of previously reserved balances. The 1998 amount
also includes a $207,000 recovery against the Master Lease agreement with CRCA.
See Note 4 to the Partnership's financial statements included in the 1998 Form
10-K.

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

The information called for in this disclosure is not applicable to the
Registrant.


                                      13
<PAGE>   14
PART II - OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS

Reference is made to Item 3 - Legal Proceedings in the Partnership's December
31, 1998 Form 10-K for a discussion of material legal proceedings involving the
Partnership.

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)  Exhibits

See Exhibit Index.

(b)  Reports on Form 8-K

None.

                                      14
<PAGE>   15
 
                                   SIGNATURES


Pursuant to the requirements of the Securities Act of 1934, the Registrant has
duly caused this report to be signed on its behalf by the undersigned thereunto
duly authorized, on the 10th day of May 1999.





                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                    Registrant





            By:     /s/ DONALD D. TORISKY 
                    -----------------------------------
                    Donald D. Torisky 
                    Chairman and Chief Executive Officer,
                    Lease Resolution Corporation 
                    General Partner of Datronic
                    Equipment Income Fund XX, L.P.




            By:     /s/ ROBERT P. SCHAEN   
                    -----------------------------------
                    Robert P. Schaen
                    Vice-Chairman and Chief Financial Officer, 
                    Lease Resolution Corporation, 
                    General Partner of Datronic Equipment Income Fund XX, L.P.


<PAGE>   16
                               INDEX TO EXHIBITS
 

<TABLE>
<CAPTION>
EXHIBIT 
NUMBER                         DESCRIPTION
-------                        -----------
  <S>               <C>
  27                Financial Data Schedule, which is submitted electronically
                    to the Securities and Exchange Commission for Information
                    only and not filed.
</TABLE>