United States
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                   FORM 10-QSB


              [X] QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                  For the quarterly period ended June 30, 1996

                                       OR

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

         For the transition period from...............to...............

                         Commission file number 0-16574

               ENEX OIL & GAS INCOME PROGRAM III - SERIES 6, L.P.
        (Exact name of small business issuer as specified in its charter)

                        New Jersey                           76-0214443
            (State or other jurisdiction of               (I.R.S. Employer
             incorporation or organization)              Identification No.)

                         Suite 200, Three Kingwood Place
                              Kingwood, Texas 77339
                    (Address of principal executive offices)

                           Issuer's telephone number:
                                 (713) 358-8401

         Check whether the issuer (1) filed all reports  required to be filed by
Section 13 or 15(d) of the  Exchange  Act during the past 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

Transitional Small Business Disclosure Format (Check one):

                                    Yes   No X





                              PART I. FINANCIAL INFORMATION

Item 1. Financial Statements



ENEX OIL & GAS INCOME PROGRAM III - SERIES 6, L.P.
BALANCE SHEET
- ------------------------------------------------------------------------------------

                                                                   JUNE 30,
ASSETS                                                               1996
                                                               ---------------
                                                                  (Unaudited)
CURRENT ASSETS:
                                                                       
  Cash                                                         $        5,015
  Accounts receivable - oil & gas sales                                39,404
  Other current assets                                                 44,961
                                                               ---------------

Total current assets                                                   89,380
                                                               ---------------

OIL & GAS PROPERTIES
  (Successful efforts accounting method) - Proved
   mineral interests and related equipment & facilities             2,754,315
  Less  accumulated depreciation and depletion                      2,516,260
                                                               ---------------

Property, net                                                         238,055
                                                               ---------------


TOTAL                                                          $      327,435
                                                               ===============

LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Accounts payable                                            $       36,184
   Payable to general partner                                          27,520
                                                               ---------------

Total current liabilities                                              63,704
                                                               ---------------

NONCURRENT PAYABLE TO GENERAL PARTNER                                  55,041
                                                               ---------------

PARTNERS' CAPITAL:
   Limited partners                                                   144,106
   General partner                                                     64,584
                                                               ---------------

Total partners'capital                                                208,690
                                                               ---------------

TOTAL                                                          $      327,435
                                                               ===============





See accompanying notes to financial statements.
- ------------------------------------------------------------------------------

                                       I-1





ENEX OIL & GAS INCOME PROGRAM III - SERIES 6, L.P.
STATEMENTS OF OPERATIONS


(UNAUDITED)                                 QUARTER ENDED                                                SIX MONTHS ENDED

                                  JUNE 30,      JUNE 30,      JUNE 30,                        JUNE 30,
                                   1996           1995          1996        1995

REVENUES:
                                                                   
  Oil and gas sales             $  87,465     $   87,473     $ 186,762   $ 189,491
                                ----------     ---------     ---------   ----------
EXPENSES:
  Depreciation and depletion       19,394         34,050        38,858      74,897
  Impairment of property                -              -       194,403           -
  Lease operating expenses         41,065         49,708        93,152      96,024
  Production taxes                  5,172          5,229        11,321      10,967
  General and administrative       10,937         15,536        23,816      30,313
                                 --------        --------     --------    ---------
Total expenses                     76,568        104,523       361,550     212,201
                                 --------        --------     --------    ---------
INCOME (LOSS) FROM OPERATIONS      10,897        (17,050)     (174,788)    (22,710)
                                 --------        --------     --------    ---------
OTHER INCOME:
  Gain on sale of property         36,722              -        37,378           -
                                 --------        --------      -------     ---------
NET INCOME (LOSS)             $    47,619    $    (17,050)  $ (137,410)   $(22,710)
                                 ========        =========     ========    ==========







See accompanying notes to financial statements.

                                       I-2




ENEX OIL AND GAS INCOME PROGRAM III - SERIES 5, L.P.
STATEMENTS OF CASH FLOWS

(UNAUDITED)
                                                     SIX MONTHS ENDED
                                                 --------------------------
                                                 JUNE 30,          JUNE 30,
                                                  1996              1995
CASH FLOWS FROM OPERATING ACTIVITIES:          ----------       -----------
                                                          
Net income (loss)                             $ (137,410)      $ (22,710)
                                               ----------        ----------
Adjustments to reconcile net income (loss)
 to net cash  provided by operating
   activities:
  Depreciation and depletion                      38,858           74,897
  Impairment of property                         194,403               -
  Gain on sale of property                       (37,378)              -
(Increase) in:
  Accounts receivable - oil & gas sales          (10,033)              75
  Other current assets                           (41,633)            (981)
Increase (decrease) in:
   Accounts payable                                 6,836          (6,303)
   Payable to affiliated limited partnership           -            1,013
   Payable to general partner                    (41,821)         (10,375)
                                                 --------         -------
Total adjustments                                109,232           58,326

Net cash provided (used) by operating activities (28,178)          35,616
                                                  -------          -------
CASH FLOWS FROM INVESTING ACTIVITIES:
    Proceeds from sale of property                 52,366               -
    Property additions - development costs        (24,678)         (1,100)
                                                   -------         -------
Net cash provided (used) by investing activities   27,688          (1,100)

CASH FLOWS FROM FINANCING ACTIVITIES:
   Cash distributions                                   -         (35,948)
                                                   -------         -------
NET (DECREASE) IN CASH                               (490)         (1,432)

CASH AT BEGINNING OF YEAR                           5,505           3,248
                                                 --------         --------
CASH AT END OF PERIOD                          $    5,505        $  1,816
                                                 ========         ========




See accompanying notes to financial statements.

                                       I-3



ENEX OIL & GAS INCOME PROGRAM III - SERIES 6, L.P.

NOTES TO UNAUDITED FINANCIAL STATEMENTS

1.       The  interim  financial   information  included  herein  is  unaudited;
         however,  such information reflects all adjustments  (consisting solely
         of  normal  recurring   adjustments)  which  are,  in  the  opinion  of
         management,  necessary  for a fair  presentation  of  results  for  the
         interim periods.

2.       Effective  February  1,  1996,  the Company sold its  interest  in the
         Credo acquisition  for $10,500.  The  Company  recognized  a $656 gain
         from the sale.  Effective April 1, 1996, the Company sold its interest
         in the Kidd well in the Enexco  acquisition for $22,400.  The Company
         recognized a $21,253 gain from the sale. Effective 6/1/96, the Company
         sold its interest in the Harper well in the RIC acquisition for
         $19,466.  The Company  recognized a gain of $15,469 from the sale.

3.      On August 9, 1996, the Company's General Partner submitted  preliminary
         proxy material to the Securities Exchange Commission with respect to a
         proposed consolidation of the Company with 33 other managed  limited 
         partnerships.  The terms and conditions of the proposed  consolidation
         are set forth in such preliminary proxy material.


                                       I-4



Item 2.  Management's Discussion and Analysis or Plan of Operation.


Second Quarter 1995 Compared to Second Quarter 1996

Oil and gas  sales for the  second  quarter  remained  relatively  unchanged  at
$87,465 in 1996 as compared to $87,473 in 1995.  Oil sales  increased  by $2,502
(4%).  A 6% increase in the average oil sales price  increased  sales by $3,921.
This increase was partially offset by a 2% decrease in oil production. Gas sales
decreased by $2,510  (11%).  A 37% decrease in gas  production  reduced sales by
$8,676.  This decrease was partially offset by a 42% increase in the average gas
sales price. The changes in the average sales prices  correspond with changes in
the overall  market for the sale of oil and gas. The decrease in oil  production
was  primarily  a result of natural  production  declines,  partially  offset by
production  from the  Corkscrew  acquisition  which had been shut-in  during the
second  quarter of 1995 for rod  repairs.  The  decrease in gas  production  was
primarily the result of the sale of the Credo  acquisition  in the first quarter
of 1996 and the sale of the Kidd  well in the  Enex  acquisition  in the  fourth
quarter of 1995, coupled with natural production declines.

Lease operating expenses decreased to $41,065 in the second quarter of 1996 from
$49,708 in the second quarter of 1995. The decrease of $8,643 (21%) is primarily
due to workover expenses incurred on the Corkscrew acquisition in 1995.

Depreciation and depletion expense decreased to $19,394 in the second quarter of
1996 from $34,050 in the second quarter of 1995.  This  represents a decrease of
$14,656 (43%). The changes in production,  noted above,  caused depreciation and
depletion  expense to decrease by $5,460,  while a 32% decrease in the depletion
rate reduced  depreciation and depletion  expense by an additional  $9,196.  The
rate decrease was primarily due to the lower property  basis  resulting from the
recognition  of an  impairment  of property for $194,403 in the first quarter of
1996.

Effective  April 1, 1996,  the Company sold its interest in the Kidd well in the
Enexco  acquisition for $22,400.  The Company recognized a $21,253 gain from the
sale.  Effective 6/1/96, the Company sold its interest in the Harper well in the
RIC acquisition for $19,466.  The Company  recognized a gain of $15,469 from the
sale.

General and  administrative  expenses decreased to $10,937 in the second quarter
of 1996 from  $15,536 in the second  quarter of 1995.  This  decrease  of $4,599
(30%) is primarily due to less staff time being required to manage the Company's
operations.

First Six Months in 1995 Compared to First Six Months in 1996

Oil and gas sales for the first six months  decreased  to  $186,762 in 1996 from
$189,491 in 1995. This represents a decrease of $2,729 (1%). Oil sales decreased
by $8,246 (6%). A 12% decrease in oil production reduced sales by $16,553.  This
decrease was partially offset by a 7% increase

                                       I-5





in the average oil sales  price.  Gas sales  increased  by $5,517  (11%).  A 32%
increase  in the  average  gas sales  price  increased  sales by  $13,077.  This
increase was partially  offset by a 16% decrease in gas production.  The changes
in the average sales prices  correspond  with changes in the overall  market for
the sale of oil and gas. The decrease in oil  production  was primarily a result
of  natural  production  declines,  partially  offset  by  production  from  the
Corkscrew  acquisition  which had been shut-in during the second quarter of 1995
for rod repairs.  The decrease in gas production was primarily the result of the
sale of the Credo  acquisition  in the first quarter of 1996 and the sale of the
Kidd well in the Enex  acquisition  in the fourth  quarter of 1995  coupled with
natural production declines.

Lease operating expenses decreased to $93,152 in the first six months of 1996 to
$96,024  in the  first six  months  of 1995.  The  decrease  of  $2,872  (3%) is
primarily  due to workover  expenses  incurred on the Corkscrew  acquisition  in
1995.

Depreciation and depletion  expense decreased to $38,858 in the first six months
of 1996 from $74,897 in the first six months of 1995. This represents a decrease
of $36,039 (48%). The changes in production,  noted above,  caused  depreciation
and  depletion  expense to  decrease  by  $9,779,  while a 40%  decrease  in the
depletion  rate reduced  depreciation  and  depletion  expense by an  additional
$26,260.  The rate  decrease  was  primarily  due to the  lower  property  basis
resulting from the  recognition of an impairment of property for $194,403 in the
first quarter of 1996.

Effective  February  1,  1996,  the  Company  sold  its  interest  in the  Credo
acquisition  for  $10,500.  The  Company  recognized  a $656 gain from the sale.
Effective  April 1, 1996,  the Company sold its interest in the Kidd well in the
Enexco  acquisition for $22,400.  The Company recognized a $21,253 gain from the
sale.  Effective 6/1/96, the Company sold its interest in the Harper well in the
RIC acquisition for $19,466.  The Company  recognized a gain of $15,469 from the
sale.

The  Financial  Accounting  Standards  Board has issued  Statement  of Financial
Accounting  Standard  ("SFAS")  No.  121,  "Accounting  for  the  Impairment  of
Long-Lived  Assets and for Long- Lived Assets to be Disposed Of," which requires
certain assets to be reviewed for impairment  whenever  events or  circumstances
indicate the carrying  amount may not be  recoverable.  In the first  quarter of
1996,  the Company  recognized a non-cash  impairment  provision of $194,403 for
certain  oil and gas  properties  due to market  indications  that the  carrying
amounts were not fully recoverable.

General and administrative expenses decreased to $23,816 in the first six months
of 1996 from  $30,313 in the first six months of 1995.  This  decrease of $6,497
(21%) is primarily due to less staff time being required to manage the Company's
operations.

                                       I-6




CAPITAL RESOURCES AND LIQUIDITY

The  Company's  cash  flow is a direct  result  of the  amount  of net  proceeds
realized from the sale of oil and gas  production  after the payment of its debt
obligations.  Accordingly,  the  changes  in cash  flow  from  1995 to 1996  are
primarily  due to the changes in oil and gas sales  described  above.  It is the
general  partner's  intention to distribute  substantially  all of the Company's
remaining available cash flow to the Company's partners.

The Company will continue to recover its reserves and  distribute to the limited
partners the net proceeds realized from the sale of oil and gas production after
the payment of its debt obligations.  Distribution amounts are subject to change
if net  revenues  are greater or less than  expected.  Nonetheless,  the general
partner  believes the Company will continue to have sufficient cash flow to fund
operations and to maintain a regular pattern of distributions.

On August 9, 1996, the Company's  General Partner  submitted  preliminary  proxy
material  to the  Securities  Exchange  Commission  with  respect  to a proposed
consolidation  of the Company with 33 other managed  limited  partnerships.  The
terms  and  conditions  of the  proposed  consolidation  are set  forth  in such
preliminary proxy material.

As of June 30,  1996,  the  Company  had no  material  commitments  for  capital
expenditures.  The  Company  does  not  intend  to  engage  in  any  significant
developmental drilling activity.


                                       I-7






                           PART II. OTHER INFORMATION


         Item 1.   Legal Proceedings.

                   None

         Item 2.   Changes in Securities.

                   None

         Item 3.   Defaults Upon Senior Securities.

                   Not Applicable

         Item 4.   Submission of Matters to a Vote of Security Holders.

                   Not Applicable

         Item 5.   Other Information.

                   Not Applicable

         Item 6.   Exhibits and Reports on Form 8-K.

                   (a)  There are no exhibits to this report.

                   (b)   The  Company  filed no  reports  on Form 8-K during the
                         quarter ended June 30, 1996.


                                      II-1





                                   SIGNATURES


         In accordance with the requirements of the Exchange Act, the registrant
caused this report to be signed on its behalf by the undersigned  thereunto duly
authorized.


                                                 ENEX OIL & GAS INCOME
                                            PROGRAM III - SERIES 6, L.P.
                                            ---------------------------
                                                     (Registrant)



                                             By:ENEX RESOURCES CORPORATION
                                                --------------------------
                                                    General Partner



                                             By: /s/ R. E. Densford
                                                 ------------------
                                                     R. E. Densford
                                               Vice President, Secretary
                                             Treasurer and Chief Financial
                                                        Officer




August 13, 1996                              By: /s/ James A. Klein
                                                -------------------
                                                      James A. Klein
                                                  Controller and Chief
                                                   Accounting Officer