UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549

                                   FORM 10-Q

(Mark One)

[XX]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
      EXCHANGE ACT OF 1934
   

For the quarterly period ended      June 30, 1996
                               -----------------------------------------------


                                     OR

[__]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
      EXCHANGE ACT OF 1934

For the transition period from                      to
                              ----------------------  -------------------------
            
                              ----------------------
 

For Quarter Ended June 30, 1996                    Commission File No. 0-16512

              American Income Partners III-B Limited Partnership
- -------------------------------------------------------------------------------
            (Exact name of registrant as specified in its charter
 

Massachusetts                                                    04-2968859
- ----------------------------------------------------         ------------------
(State or other jurisdiction of                              (IRS Employer
 incorporation or organization)                              Identification No.)
 
98 North Washington Street, Boston, MA                             02114
- ----------------------------------------------------         ------------------
(Address of principal executive offices)                        (Zip Code)
 
Registrant's telephone number, including area code             (617) 854-5800
                                                             ------------------
 
- --------------------------------------------------------------------------------
(Former name, former address and former fiscal year, if changed since 
                                 last report.)


  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. Yes    X    No
                                             ---------  ---------     

               APPLICABLE ONLY TO ISSUERS INVOLVED IN BANKRUPTCY
                  PROCEEDINGS DURING THE PRECEDING FIVE YEARS

  Indicate by check mark whether the registrant has filed all documents and
reports required to be filed by Sections 12, 13, or 15(d) of the Securities
Exchange Act of 1934 subsequent to the distribution of securities under a plan
confirmed by a court 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. Yes         No
                                                     ---------  ---------  

                                       1

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                                   FORM 10-Q

                                     INDEX



PART I.  FINANCIAL INFORMATION:                                           Page
                                                                          ----


 
 
     Item 1.  Financial Statements
                                                                 
 
        Statement of Financial Position
         at June 30, 1996 and December 31, 1995                              3
 
        Statement of Operations
         for the three and six months ended June 30, 1996 and 1995           4
 
        Statement of Cash Flows
         for the six months ended June 30, 1996 and 1995                     5
 
        Notes to the Financial Statements                                  6-8


     Item 2.  Management's Discussion and Analysis of
              Financial Condition and Results of Operations               9-12


PART II.  OTHER INFORMATION:

     Items 1 - 6                                                            13


                                       2

 
              AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                        STATEMENT OF FINANCIAL POSITION
                      June 30, 1996 and December 31, 1995

                                  (Unaudited)


 
 
                                           June 30,    December 31,
                                             1996          1995
                                          -----------  ------------
                                                 
ASSETS
- ------ 
 
Cash and cash equivalents                  $  735,121    $  802,718
Rents receivable, net of allowance for
 doubtful accounts of $60,000 at                
 December 31, 1995                              3,301         3,044  
    
Accounts receivable - affiliate                 4,129         5,490

Equipment at cost, net of accumulated
 depreciation of $8,654,683 and 
 $7,839,693 at June 30, 1996 and                
 December 31, 1995, respectively            2,803,238     3,684,320 
                                           ----------    ----------
    
   Total assets                            $3,545,789    $4,495,572
                                           ==========    ==========
 
LIABILITIES AND PARTNERS' CAPITAL
- ---------------------------------
 
Accrued liabilities                        $   11,750    $   20,000
Accrued liabilities - affiliate                 4,720        15,216
Deferred rental income                         53,844        52,247
Cash distributions payable to partners        213,508       213,508
                                           ----------    ----------
   Total liabilities                          283,822       300,971
                                           ----------    ----------
Partners' capital (deficit):
   General Partners                          (215,251)     (205,925)
   Limited Partnership Interests
   (1,127,330 Units; initial purchase       
    price of $25 each)                      3,477,218     4,400,526    
                                           ----------    ----------
   Total partners' capital                  3,261,967     4,194,601
                                           ----------    ----------
   Total liabilities and partners'       
    capital                                $3,545,789    $4,495,572
                                           ==========    ==========
 


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

                                       3

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                            STATEMENT OF OPERATIONS
           for the three and six months ended June 30, 1996 and 1995

                                  (Unaudited)


 
 
                                              Three months                 Six Months
                                              Ended June 30,              Ended June 30,
                                          1996             1995          1996        1995
                                     ---------------  --------------  -----------  ---------
                                                                       
 
Income:
   Lease revenue                          $ 199,912         $284,598   $ 407,656    $524,525
   Interest income                           10,200           11,010      19,544      22,055
   Gain on sale of equipment                  6,519           20,090       6,609     281,012
                                          ---------         --------   ---------    --------
   Total income                             216,631          315,698     433,809     827,592
                                          ---------         --------   ---------    --------
 
Expenses:
   Depreciation                             136,790          177,099     275,131     354,971
   Write-down of equipment                  600,000               --     600,000          --
   Interest expense                              --              222          --         710
   Equipment management fees
       - affiliate                            9,996           14,230      20,383      26,226
   Operating expenses - affiliate            24,758           31,419      43,913      66,808
                                          ---------         --------   ---------    --------
   Total expenses                           771,544          222,970     939,427     448,715
                                          ---------         --------   ---------    --------
 
Net income (loss)                         $(554,913)        $ 92,728   $(505,618)   $378,877
                                          =========         ========   =========    ========
 
Net income (loss)                         
   per limited partnership unit           $   (0.49)        $   0.08    $  (0.44)   $   0.33
                                          =========         ========   =========    ========
 
Cash distributions declared
   per limited partnership unit           $    0.19         $   0.31   $    0.37    $   0.62
                                          =========         ========   =========    ========
 


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

                                       4

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                            STATEMENT OF CASH FLOWS
                for the six months ended June 30, 1996 and 1995

                                  (Unaudited)


 
 
                                             1996          1995
                                          -----------  ------------
                                                 
 
Cash flows from (used in) operating
 activities:                               
Net income (loss)                          $(505,618)  $   378,877
Adjustments to reconcile net income
 (loss) to net cash from operating
 activities:                                
   Depreciation                              275,131       354,971
   Write-down of equipment                   600,000            --
   Gain on sale of equipment                  (6,609)     (281,012)
   Decrease in allowance for doubtful        
    accounts                                 (60,000)           --  
Changes in assets and liabilities
 Decrease in:
   rents receivable                           59,743       191,711
   accounts receivable - affiliate             1,361        77,738
Increase (decrease) in:
   accrued interest                               --        (8,497)
   accrued liabilities                        (8,250)         (500)
   accrued liabilities - affiliate           (10,496)        5,241
   deferred rental income                      1,597         2,254
                                           ---------   -----------
   Net cash from operating activities        346,859       720,783
                                           ---------   -----------
Cash flows from investing activities:
   Proceeds from equipment sales              12,560       281,012
                                           ---------   -----------
   Net cash from investing activities         12,560       281,012
                                           ---------   -----------
Cash flows used in financing activities:
     Principal payments - notes payable           --      (212,146)
   Distributions paid                       (427,016)     (925,207)
                                           ---------   -----------
   Net cash used in financing activities    (427,016)   (1,137,353)
                                           ---------   -----------
Net decrease in cash and cash                
 equivalents                                 (67,597)     (135,558)          
Cash and cash equivalents at beginning
 of period                                   802,718       958,005
                                           ---------   -----------
Cash and cash equivalents at end of       
 period                                    $ 735,121   $   822,447
                                           =========   ===========
 
Supplemental disclosure of cash flow
 information:                             
   Cash paid during the period for         
    interest                               $      --   $     9,207
                                           =========   ===========
    


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

                                       5

               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                       Notes to the Financial Statements

                                 June 30, 1996
                                  (Unaudited)



NOTE 1 - BASIS OF PRESENTATION
- ------------------------------

  The financial statements presented herein are prepared in conformity with
generally accepted accounting principles and the instructions for preparing Form
10-Q under Rule 10-01 of Regulation S-X of the Securities and Exchange
Commission and are unaudited.  As such, these financial statements do not
include all information and footnote disclosures required under generally
accepted accounting principles for complete financial statements and,
accordingly, the accompanying financial statements should be read in conjunction
with the footnotes presented in the 1995 Annual Report.  Except as disclosed
herein, there has been no material change to the information presented in the
footnotes to the 1995 Annual Report.

  In the opinion of management, all adjustments (consisting of normal and
recurring adjustments) considered necessary to present fairly the financial
position at June 30, 1996 and December 31, 1995 and results of operations for
the three and six month periods ended June 30, 1996 and 1995 have been made and
are reflected.


NOTE 2 - CASH
- -------------

  At June 30, 1996, the Partnership had $730,000 invested in reverse repurchase
agreements secured by U.S. Treasury Bills or interests in U.S. Government
securities.


NOTE 3 - REVENUE RECOGNITION
- ----------------------------

  Rents are payable to the Partnership monthly, quarterly or semi-annually and
no significant amounts are calculated on factors other than the passage of time.
The leases are accounted for as operating leases and are noncancellable. Rents
received prior to their due dates are deferred.  Future minimum rents of
$997,861 are due as follows:


 
                                     
        For the year ending June 30, 1997   $632,299
                                     1998    232,221
                                     1999     61,542
                                     2000     61,542
                                     2001     10,257
                                            --------
                                    Total   $997,861
                                            ========
       
 


                                       6

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                       Notes to the Financial Statements

                                  (Continued)


NOTE 4 - EQUIPMENT
- ------------------

  The following is a summary of equipment owned by the Partnership at June 30,
1996.  In the opinion of American Finance Group ("AFG"), the acquisition cost of
the equipment did not exceed its fair market value.


 
                           Lease Term            Equipment
Equipment Type              (Months)              at Cost
- --------------             ----------            --------- 

 
                                       
Aircraft                     36-108             $ 8,412,409
Motor vehicles                12-72               1,171,572
Manufacturing                 24-72                 663,153
Communications                 1-60                 618,182
Locomotives                   57-60                 406,969
Materials handling             1-84                 185,636
                                                 ----------
 
                          Total equipment cost   11,457,921
 
                      Accumulated depreciation   (8,654,683)
                                                -----------
 
    Equipment, net of accumulated depreciation  $ 2,803,238
                                                ===========


  At June 30, 1996, the Partnership's equipment portfolio included equipment
having a proportionate original cost of $9,993,535, representing approximately
87% of total equipment cost.

  The summary above includes fully depreciated equipment with a cost of
approximately $79,000 which is not subject to an active lease agreement.

  During the quarter ended June 30, 1996, the Partnership recorded a write-down,
representing an impairment in value, pertaining to its interest in a Lockheed L-
1011 aircraft.   This adjustment was precipitated by continuing deterioration in
the secondary market for wide-body aircraft of this type.  Several air carriers
have reduced their commitment to the L-1011 and, currently, a major domestic air
carrier is expected to retire eleven L-1011 aircraft from its fleet.  Further,
it appears that future demand for this type of aircraft will be  weak,
consisting  principally of air cargo carriers or operators of passenger
charters.  In consideration of such circumstances and in accordance with
Financial Accounting Standards Board Statement No. 121, Accounting for the
Impairment of Long-Lived Assets and for Long-Lived Assets to be Disposed Of, the
Partnership reduced the carrying value of its L-1011 aircraft interest to its
estimated current fair market value.  This resulted in a write-down of $600,000,
representing $0.53 per limited partnership unit.


NOTE 5 - RELATED PARTY TRANSACTIONS
- -----------------------------------

  All operating expenses incurred by the Partnership are paid by AFG on behalf
of the Partnership and AFG is reimbursed at its actual cost for such
expenditures.  Fees and other costs incurred during each of the six month
periods ended June 30, 1996 and 1995, which were paid or accrued by the
Partnership to AFG or its Affiliates, are as follows:

                                       7

 
              AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                       Notes to the Financial Statements

                                  (Continued)



 
                                     1996      1995
                                   --------  --------
                                       
 
Equipment management fees           $20,383   $26,226
Administrative charges               10,500    10,500
Reimbursable operating expenses
 due to third parties                33,413    56,308
                                    -------   -------
 
  Total                             $64,296   $93,034
                                    =======   =======


  All rents and proceeds from the sale of equipment are paid directly to either
AFG or to a lender.  AFG temporarily deposits collected funds in a separate
interest-bearing escrow account prior to remittance to the Partnership.  At June
30, 1996, the Partnership was owed $4,129 by AFG for such funds and the interest
thereon.  These funds were remitted to the Partnership in July 1996.

NOTE 6 - LEGAL PROCEEDINGS
- --------------------------

  On March 15, 1993, Herman's Sporting Goods, Inc., a lessee of the Partnership
(the "Debtor"), filed for protection under Chapter 11 of the Bankruptcy Code in
the United States District Court, Trenton, New Jersey (the "District Court").
Certain unpaid rents due to the Partnership were scheduled by the Debtor as
unsecured claims.  Upon order of the District Court, renewal rental schedules
for all equipment leased to the Debtor by the Partnership were executed and are
currently in effect.  On August 23, 1994, the District Court confirmed the
Debtor's First Modified Plan of Reorganization, as Amended and Modified.  On
April 26, 1996, the Debtor refiled for protection under Chapter 11 of the
Bankruptcy Code in the District Court.  Rents due to the Partnership pursuant to
the renewal schedules due to expire on June 30, 1996 were scheduled by the
Debtor as unsecured claims.  At June 30, 1996, the Partnership was due $2,356
from the Debtor with respect to its 1993 and 1996 unsecured claims.  The
Partnership's equipment portfolio includes equipment on lease to the Debtor with
an original cost of approximately $31,292, which is expected to be purchased by
the Debtor, and is fully depreciated for financial reporting purposes.  This
equipment represents less than 1% of the Partnership's aggregate equipment
portfolio at June 30, 1996.  These Bankruptcies did not have a material adverse
effect on the financial position of the Partnership.

                                       8

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                                   FORM 10-Q

                         PART I. FINANCIAL INFORMATION



Item 2.  Management's Discussion and Analysis of Financial Condition and Results
- --------------------------------------------------------------------------------
of Operations.
- --------------

Three and six months ended June 30, 1996 compared to the three and six months
- -----------------------------------------------------------------------------
ended June 30, 1995:
- --------------------

Overview
- --------

  The Partnership was organized in 1987 as a direct-participation equipment
leasing program to acquire a diversified portfolio of capital equipment subject
to lease agreements with third parties.  The Partnership's stated investment
objectives and policies contemplated that the Partnership would wind-up its
operations within approximately seven years of its inception.  Accordingly, the
Managing General Partner is pursuing the remarketing of all of the Partnership's
remaining equipment and has engaged an investment adviser to solicit interested
third-party buyers.  This effort is being undertaken in conjunction with certain
other affiliated partnerships and, if successful, would result in the sale of
each affected partnership's assets to a selected buyer.  The Managing General
Partner believes this approach will (i) maximize the disposition prices of each
partnership's assets and (ii) prevent the incidence of future expenses to
operate a publicly-registered limited partnership with a declining asset base.
The Managing General Partner is evaluating expressions of interest submitted by
the investment adviser from a number of potential buyers, but is under no
obligation to accept any proposal.  If successful, the Managing General Partner
anticipates that it would wind-up the operations of the Partnership and make a
liquidating distribution to the Partners, net of any cash reserves which the
Managing General Partner may consider appropriate, on or before December 31,
1996.

Results of Operations
- ---------------------

  For the three and six months ended June 30, 1996, the Partnership recognized
lease revenue of $199,912 and $407,656, respectively, compared to $284,598 and
$524,525 for the same periods in 1995.  The decrease in lease revenue from 1995
to 1996 was expected and resulted principally from primary lease term
expirations and the sale of equipment.  The Partnership also earns interest
income from temporary investments of rental receipts and equipment sales
proceeds in short-term instruments.

  The Partnership's equipment portfolio includes certain assets in which the
Partnership holds a proportionate ownership interest.  In such cases, the
remaining interests are owned by AFG or an affiliated equipment leasing program
sponsored by AFG.  Proportionate equipment ownership enables the Partnership to
further diversify its equipment portfolio by participating in the ownership of
selected assets, thereby reducing the general levels of risk which could result
from a concentration in any single equipment type, industry or lessee.  The
Partnership and each affiliate individually report, in proportion to their
respective ownership interests, their respective shares of assets, liabilities,
revenues, and expenses associated with the equipment.

  During the three months ended June 30, 1996, the Partnership sold equipment
having a net book value of $5,951 to existing lessees and third parties. These
sales resulted in a net gain, for financial statement purposes, of $6,519
compared to a net gain of $20,090 on equipment which had been fully depreciated
for the same period in 1995.

  During the six months ended June 30, 1996, the Partnership sold equipment
having a net book value of $5,951 to existing lessees and third parties.  These
sales resulted in a net gain, for financial statement purposes, of $6,609
compared to a net gain of $281,012 on equipment which had been fully depreciated
for the same period in 1995.

  It cannot be determined whether future sales of equipment will result in a net
gain or a net loss to the Partnership, as such transactions will be dependent
upon the condition and type of equipment being sold and its marketability at the

                                       9


              AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                                   FORM 10-Q

                        PART I.  FINANCIAL INFORMATION
 

time of sale. In addition, the amount of gain or loss reported for financial
statement purposes is partly a function of the amount of accumulated
depreciation associated with the equipment being sold.

  The ultimate realization of residual value for any type of equipment is
dependent upon many factors, including AFG's ability to sell and re-lease
equipment.  Changing market conditions, industry trends, technological advances,
and many other events can converge to enhance or detract from asset values at
any given time.  AFG attempts to monitor these changes in order to identify
opportunities which may be advantageous to the Partnership and which will
maximize total cash returns for each asset.

  The total economic value realized upon final disposition of each asset is
comprised of all primary lease term revenue generated from that asset, together
with its residual value.  The latter consists of cash proceeds realized upon the
asset's sale in addition to all other cash receipts obtained from renting the
asset on a re-lease, renewal or month-to-month basis.  The Partnership
classifies such residual rental payments as lease revenue.  Consequently, the
amount of gain or loss reported in the financial statements is not necessarily
indicative of the total residual value the Partnership achieved from leasing the
equipment.

  Depreciation expense for the three and six months ended June 30, 1996 was
$136,790 and $275,131, respectively, compared to $177,099 and $354,971 for the
same periods in 1995.  For financial reporting purposes, to the extent that an
asset is held on primary lease term, the Partnership depreciates the difference
between (i) the cost of the asset and (ii) the estimated residual value of the
asset on a straight-line basis over such term.  For purposes of this policy,
estimated residual values represent estimates of equipment values at the date of
primary lease expiration.  To the extent that an asset is held beyond its
primary lease term, the Partnership continues to depreciate the remaining net
book value of the asset on a straight-line basis over the asset's remaining
economic life.

  During the quarter ended June 30, 1996, the Partnership recorded a write-down,
representing an impairment in value, pertaining to its interest in a Lockheed L-
1011 aircraft.   This adjustment was precipitated by continuing deterioration in
the secondary market for wide-body aircraft of this type.  Several air carriers
have reduced their commitment to the L-1011 and, currently, a major domestic air
carrier is expected to retire eleven L-1011 aircraft from its fleet.  Further,
it appears that future demand for this type of aircraft will be  weak,
consisting  principally of air cargo carriers or operators of passenger
charters.  In consideration of such circumstances and in accordance with
Financial Accounting Standards Board Statement No. 121, Accounting for the
Impairment of Long-Lived Assets and for Long-Lived Assets to be Disposed Of, the
Partnership reduced the carrying value of its L-1011 aircraft interest to its
estimated current fair market value.  This resulted in a write-down of $600,000,
representing $0.53 per limited partnership unit.

  Interest expense was $222 and $710 or less than 1% of lease revenue for each
of the three and six month periods ended June 30, 1995.    Management fees were
5% of lease revenue in each of the periods ended June 30, 1996 and 1995 and will
not change as a percentage of lease revenue in future periods.

  Operating expenses consist principally of administrative charges, professional
service costs, such as audit and legal fees, as well as printing, distribution
and remarketing expenses.  In certain cases, equipment storage or repairs and
maintenance costs may be incurred in connection with equipment being remarketed.
Collectively, operating expenses represented approximately 12.4% and 10.8% of
lease revenue for the three and six month periods ended June 30, 1996,
respectively, compared to 11% and 12.7% of lease revenue for the same periods in
1995. The amount of future operating expenses cannot be predicted with
certainty; however, such expenses are usually higher during the acquisition and
liquidation phases of a partnership.  Other fluctuations typically occur in
relation to the volume and timing of remarketing activities.

                                       10

              AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                                   FORM 10-Q

                        PART I.  FINANCIAL INFORMATION
                               
 
Liquidity and Capital Resources and Discussion of Cash Flows
- ------------------------------------------------------------

  The Partnership by its nature is a limited life entity which was established
for specific purposes described in the preceding "Overview".  As an equipment
leasing program, the Partnership's principal operating activities derive from
asset rental transactions.  Accordingly, the Partnership's principal source of
cash from operations is provided by the collection of periodic rents.  These
cash inflows are used to satisfy debt service obligations associated with
leveraged leases, and to pay management fees and operating costs.  Operating
activities generated net cash inflows of $346,859 and $720,783 during the six
months ended June 30, 1996 and 1995, respectively.  Future renewal, re-lease and
equipment sale activities will cause a gradual decline in the Partnership's
lease revenue and corresponding sources of operating cash.  Overall, expenses
associated with rental activities, such as management fees, and net cash flow
from operating activities will decline as the Partnership experiences a higher
frequency of remarketing events.

  Ultimately, the Partnership will dispose of all assets under lease.  This will
occur principally through sale transactions whereby each asset will be sold to
the existing lessee or to a third party.  Generally, this will occur upon
expiration of each asset's primary or renewal/re-lease term.  In certain
instances, casualty or early termination events may result in the disposal of an
asset.  Such circumstances are infrequent and usually result in the collection
of stipulated cash settlements pursuant to terms and conditions contained in the
underlying lease agreements.

  Cash realized from asset disposal transactions is reported under investing
activities on the accompanying Statement of Cash Flows.  During the six months
ended June 30, 1996 the Partnership realized $12,560 in equipment sale proceeds
compared to $281,012 for the same period in 1995.  Future inflows of cash from
asset disposals will vary in timing and amount and will be influenced by many
factors including, but not limited to, the frequency and timing of lease
expirations, the type of equipment being sold, its condition and age, and future
market conditions.

  The Partnership obtained long-term financing in connection with certain
equipment leases.  The repayments of principal related to such indebtedness are
reported as a component of financing activities.  Each note payable is recourse
only to the specific equipment financed and to the minimum rental payments
contracted to be received during the debt amortization period (which period
generally coincides with the lease rental term).  As rental payments are
collected, a portion or all of the rental payment is used to repay the
associated indebtedness.  At June 30, 1996, the Partnership had no outstanding
indebtedness.

  Cash distributions to the General Partners and Recognized Owners are declared
and generally paid within fifteen days following the end of each calendar
quarter.  The payment of such distributions is presented as a component of
financing activities.  For the six month period ended June 30, 1996, the
Partnership declared total cash distributions of Distributable Cash From
Operations and Distributable Cash From Sales and Refinancings of $427,016.  In
accordance with the Amended and Restated Agreement and Certificate of Limited
Partnership, the Recognized Owners were allocated 99% of these distributions, or
$422,746, and the General Partners were allocated 1%, or $4,270.  The second
quarter 1996 cash distribution was paid on July 15, 1996.

  Cash distributions paid to the Recognized Owners consist of both a return of
and a return on capital.  To the extent that cash distributions consist of Cash
From Sales or Refinancings, substantially all of such cash distributions should
be viewed as a return of capital.  Cash distributions do not represent and are
not indicative of yield on investment.  Actual yield on investment cannot be
determined with any certainty until conclusion of the Partnership and will be
dependent upon the collection of all contracted rents, the generation of renewal
and/or re-lease rents, and the residual value realized for each asset at its
disposal date.  Market conditions, technological changes, the ability of AFG to

                                       11

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                                   FORM 10-Q

                         PART I. FINANCIAL INFORMATION


manage and remarket the assets, and many other events and circumstances, could
enhance or detract from individual asset yields and the collective performance
of the Partnership's equipment portfolio.

                                       12

 
               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP

                                   FORM 10-Q

                          PART II.   OTHER INFORMATION



     Item 1.           Legal Proceedings
                       Response:

                       Refer to Note 6 herein and to Note 6 in
                       the 1995 Annual Report.

     Item 2.           Changes in Securities
                       Response:  None

     Item 3.           Defaults upon Senior Securities
                       Response:  None

     Item 4.           Submission of Matters to a Vote of Security Holders
                       Response:  None

     Item 5.           Other Information
                       Response:  None

     Item 6(a).        Exhibits
                       Response:  None

     Item 6(b).        Reports on Form 8-K
                       Response:  None

                                       13

 
                                 SIGNATURE PAGE



  Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below on behalf of the registrant and in the capacity and
on the date indicated.



               AMERICAN INCOME PARTNERS III-B LIMITED PARTNERSHIP


                By:    AFG Leasing Incorporated, a Massachusetts
                       corporation and the Managing General Partner of
                       the Registrant.


                By:    /s/  Michael J. Butterfield
                       -------------------------------------
                       Michael J. Butterfield
                       Treasurer of AFG Leasing Incorporated
                       (Duly Authorized Officer and
                       Principal Accounting Officer)


                Date:  August 13, 1996
                       -------------------------------------



                By:    /s/  Gary M. Romano
                       -------------------------------------
                       Gary M. Romano
                       Clerk of AFG Leasing Incorporated
                       (Duly Authorized Officer and
                       Principal Financial Officer)


                Date:  August 13, 1996
                       -------------------------------------

                                       14