<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
                       --------------------------------


For the Quarter Ended
   March 31, 1998                               Commission File Number  0-21260
---------------------                           -------------------------------


                    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, 1998


                         PART I - FINANCIAL INFORMATION

<TABLE>
<S>                                                                <C>
Item 1.

  Index to Financial Statements

    Balance Sheets

      March 31, 1998 (unaudited)                                          3

      December 31, 1997                                                   4

    Statements of Revenue and Expenses (unaudited)

      For the three months ended March 31, 1998                           5

      For the three months ended March 31, 1997                           6

    Statements of Changes in Partners' Equity

      For the three months ended March 31, 1998                           7
        (unaudited)

    Statements of Cash Flows (unaudited)

      For the three months ended March 31, 1998                           8

      For the three months ended March 31, 1997                           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, 1998
                                  (Unaudited)



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

     ASSETS
     ------                              

     Cash and cash equivalents          $224,269    $3,808,087  $4,032,356
     Net investment in direct
       financing leases                        -       900,305     900,305
     Residual interest in CRCA                 -             -           -
     Diverted and other assets, net       15,700       216,545     232,245
     Datronic assets                           -             -           -
                                        --------    ----------  ----------
                                        
                                        $239,969    $4,924,937  $5,164,906
                                        ========    ==========  ==========


     LIABILITIES AND PARTNERS' EQUITY
     --------------------------------

     Accounts payable and
       accrued expenses                 $    222    $   12,544     $12,766
     Lessee rental deposits                  447         6,391       6,838
                                        --------    ----------  ----------
                                        
       Total liabilities                     669        18,935      19,604
                                        
     Total partners' equity              239,300     4,906,002   5,145,302
                                        --------    ----------  ----------
                                        
                                        $239,969    $4,924,937  $5,164,906
                                        ========    ==========  ==========
</TABLE>
















                See accompanying notes to financial statements.



                                       3
<PAGE>   4


                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.

                                 BALANCE SHEETS

                               December 31, 1997



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

     Cash and cash equivalents           $221,305   $3,564,194  $3,785,499
     Net investment in
       direct financing leases                  -    1,101,279   1,101,279
     Residual interest in CRCA                  -            -           -
     Diverted and other assets, net        15,700      216,545     232,245
     Datronic assets, net                       -            -           -
                                         --------   ----------  ----------
                                         
                                         $237,005   $4,882,018  $5,119,023
                                         ========   ==========  ==========


     LIABILITIES AND PARTNERS' EQUITY
     --------------------------------

     Accounts payable and
       accrued expenses                  $    355   $   17,773  $   18,128
     Lessee rental deposits                 1,916       38,461      40,377
                                         --------   ----------  ----------
                                         
          Total liabilities                 2,271       56,234      58,505
                                         
     Total partners' equity               234,734    4,825,784   5,060,518
                                         --------   ----------  ----------
                                         
                                         $237,005   $4,882,018  $5,119,023
                                         ========   ==========  ==========
</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, 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                                        $ .89          $ 1.13
                                              =====          ======
                                                             
 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, 1997
                                  (Unaudited)



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

    Revenue:
     Lease income                        $  1,068     $  80,689   $  81,757
     Interest income                        2,003        32,233      34,236
                                         --------     ---------   ---------
                                                                  
                                            3,071       112,922     115,993
                                         --------     ---------   ---------
                                         
    Expenses:                            
     Amortization of organization        
       and equipment acquisition costs      6,391        88,146      94,537
     General Partner's                   
       expense reimbursement               15,927       239,841     255,768
     Professional fees                      3,109        46,355      49,464
     Other operating expenses                 497         7,204       7,701
     Credit for lease losses               (8,428)     (116,241)   (124,669)
                                         --------     ---------   ---------
                                                                  
                                           17,496       265,305     282,801
                                         --------     ---------   ---------
                                                                  
                                                                  
    Net loss                             $(14,425)    $(152,383)  $(166,808)
                                         ========     =========   =========
                                                                  
                                                                  
    Net loss - General Partner           $   (144)    $  (1,524)  $  (1,668)
                                         ========     =========   =========
                                                                  
                                                                  
    Net loss - Limited Partners          $(14,281)    $(150,859)  $(165,140)
                                         ========     =========   =========


    Net loss per limited partnership
     unit                                  $(2.80)       $(2.14)
                                           ======        ======
                                                         
    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.

                    STATEMENT 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, 1997*  $    -      $234,734    $4,825,784  $5,060,518

    Net earnings                     848      4,520        79,416      84,784
    Allocation of General
     Partner's Equity               (848)        46           802        -
                               ---------   --------    ----------  ----------
                                           
                                           
  Balance, March 31, 1998      $    -      $239,300    $4,906,002  $5,145,302
                               =========   ========    ==========  ==========
</TABLE>




*    Balances are net of $16,232 and $292,656, 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, 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
      earnings 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.





                                       8



<PAGE>   9


                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.

                            STATEMENTS OF CASH FLOWS

                   For the three months ended March 31, 1997
                                  (Unaudited)



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

Cash flows from operating activities:
 Net loss                                $(14,425)     $ (152,383)   $ (166,808)
 Adjustments to reconcile net loss
   to net cash used in
   operating activities:
   Amortization expense                     6,391          88,146        94,537
   Credit for lease losses                 (8,428)       (116,241)     (124,669)
   Changes in assets and liabilities:
     Accounts payable and accrued
       expenses                            (1,949)        (47,019)      (48,968)
     Lessee rental deposits                  (801)            780           (21)
     Due to management company              2,306          39,066        41,372
                                         --------      ----------    ----------
                                                       
                                          (16,906)       (187,651)     (204,557)
                                         --------      ----------    ----------
                                                       
Cash flows from investing activities:                  
 Principal collections on leases           23,773         605,383       629,156
                                         --------      ----------    ----------
                                                       
Cash flows from financing activities:                  
 Distributions to Limited Partners           -           (185,672)     (185,672)
                                         --------      ----------    ----------
                                                       
Net increase in cash and                               
 cash equivalents                           6,867         232,060       238,927
                                                       
Cash and cash equivalents:                             
 Beginning of year                        198,315       2,336,816     2,535,131
                                         --------      ----------    ----------
                                                       
                                                       
 End of first quarter                    $205,182      $2,568,876    $2,774,058
                                         ========      ==========    ==========
</TABLE>














                See accompanying notes to financial statements.



                                       9



<PAGE>   10


                    DATRONIC EQUIPMENT INCOME FUND XX, L.P.
                         NOTES TO FINANCIAL STATEMENTS
                                 March 31, 1998
                                  (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 1997 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 1997 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 1997 Form 10-K.


NOTE 3 - LIMITED PARTNERSHIP DISTRIBUTIONS:

Distributions to Liquidating Limited Partners were suspended after payment of
the July 1, 1996 distribution and distributions to Continuing Limited Partners
were suspended after payment of the January 1, 1997 distribution.

NOTE 4 - SUBSEQUENT EVENT: SETTLEMENT OF LITIGATION:

On May 5, 1998, Lease Resolution Corporation (LRC), on behalf of Datronic
Equipment Income Funds XVI, XVII, XVIII, XIX, XX and Datronic Finance Income
Fund I, reached an agreement to settle all claims of the aforementioned
partnerships against Weiss & Co. ("Settlement Agreement").  (See Note 8 to the
financial statements included in the Partnership's 1997 Form 10-K).  The
Settlement Agreement is contingent upon subsequent approval by the United
States District Court dismissing Weiss & Co. as a party defendant.  Pursuant to
the terms of the Settlement Agreement, Weiss & Co. has agreed to pay LRC, on
behalf of the aforementioned partnerships, $2.4 million. LRC will determine how
these proceeds, net of contingent attorneys fees of $600,000, will be
distributed among the partnerships upon completion of the trial currently in
process against Price Waterhouse. The Settlement Agreement 

                                       10



<PAGE>   11


provides for Weiss & Co. to transfer $2.4 million to an escrow account.  This
amount will be transferred to LRC no later than 30 days following the United
States District Court entering an order of dismissal of Weiss & Co. for which no
date has yet been set.  All limited partners will be notified of the date once
it has been scheduled.










                                       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,
1997 through March 31, 1998.  The discussion and analysis of results of
operations is for the three month period ended March 31, 1998 as compared to
the corresponding period in 1997.

Liquidity and Capital Resources

During the three months ended March 31, 1998, Partnership assets continued to
be converted to cash in order to pay Partnership operating expenses, liquidate
Partnership liabilities and provide for the ultimate liquidation of the
Partnership.

During the three months ended March 31, 1998, the Partnership's cash and cash
equivalents increased by $247,000 to $4,032,000 at March 31, 1998 from
$3,785,000 at December 31, 1997.  This increase is primarily due to cash
receipts from collections on leases of $245,000 and recovery of a portion of
the Partnership's residual interest in CRCA of $207,000, partially offset by
cash used in operations of $205,000.

The Partnership's sources of liquidity on both a long-term and short-term basis
are expected to come principally from cash-on-hand and cash receipts from
leases owned by the Partnership.  The lease portfolio is scheduled to be
substantially run out by the end of 2000, unless it is determined that it is in
the Partnership's best interest to dispose of the remaining portfolio earlier
through a bulk sale.  In addition, the Partnership's sources of liquidity on a
long-term basis include proceeds from the sale of Diverted and other assets.
Management believes that its sources of liquidity in the short and long-term
are sufficient to meet its operating cash requirements, provide for ongoing
pursuit of litigation, and an orderly liquidation of the Partnership.

The continued operation and eventual liquidation of the Partnership involves
numerous complex issues which have to be resolved.  These issues relate to the
timing and realizability of lease-related assets, Diverted and other assets,
Datronic assets, litigation and the liquidation of the other Datronic
Partnerships.  These issues make it difficult to predict the time and costs
necessary to operate and liquidate the Partnership in an orderly manner.  As a
result of these uncertainties, it is unlikely that any additional distributions
will be made until all remaining assets are liquidated and the pending
litigation is resolved.  The amount of future distributions, if any, to the
Limited Partners, in all likelihood, will be significantly less than the amount
of partners' equity reflected in the March 31, 1998 balance sheets (see
Partnership's financial statements included in Item 1.)



                                       12





<PAGE>   13


Results of Operations

The Partnership had  net income of $85,000 for the three months ended March 31,
1998 in the aggregate for all classes of partners.  This compares to an
aggregate net loss for the same period in 1997 of $167,000.  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 two periods
ended March 31, 1998 and 1997 include the following:

Lease income:
Since January 1997, the Partnership has been in its Liquidation 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 for the three months ended March 31, 1998 as compared to the
corresponding period in 1997.

Interest income:
Interest income increased for the three months ended March 31, 1998 as compared
to the corresponding period in 1997 as a result of increased invested cash
balances.

Amortization of organization and equipment acquisition costs:
Amortization of organization and equipment acquisition costs ended as of May
1997 when these costs became fully amortized.

General Partner's expense reimbursement:
The decrease in the first quarter 1998 expense is primarily due to D&O
insurance and reductions in staff and related costs.  Through the first quarter
1997, insurance premiums were paid on an annual basis; however, in September
1997 a one-time premium was paid that extended coverage through the ultimate
liquidation date of the Partnership.

Professional fees:
The 1998 increase reflects fees paid in connection with the ongoing litigation
against the Partnership's former accountants which is presently scheduled for
trial in May of 1998.  This increase is partially offset by the decreasing
level of professional services required in such areas as collections,
consulting and auditing. These decreases are the result of the decrease in the
Partnership's lease portfolio and related activities.

Credit for lease losses:
The credit reflects Management's ongoing assessment of the potential losses
inherent in the lease portfolio and collections on previously reserved
balances.  The 1998 and 1997 amounts also include $207,000 and $125,000,
respectively, of recoveries on the residual interest in CRCA.  See Note 4 to
the Partnership's financial statements included in the 1997 Form 10-K.


                                       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, 1997 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 15th day of May 1998.





                                 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.    
                   








                                     15


<PAGE>   16


                                EXHIBIT INDEX
                                -------------


EXHIBIT NO.                        DESCRIPTION
-----------                        -----------
   27                              Financial Data Schedule, which is submitted  
                                   electronically to the Securities and
                                   Exchange Commission for Information only and
                                   not filed.

















                                     16