<PAGE>   1
                                                                               
================================================================================
                                                                               
                                 UNITED STATES                                 
                       SECURITIES AND EXCHANGE COMMISSION                      
                             Washington, D.C. 20549                            
                                                                               
                                   FORM 10-Q                                   
                                                                               
[X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES    
     EXCHANGE ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1996
                                                                               
                                                                               
                                                                               
[ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES   
     EXCHANGE ACT OF 1934 FOR THE TRANSITION PERIOD FROM________________
     TO __________________               
                                                                               
                                                                               
                         COMMISSION FILE NUMBER 0-11871                        
                                                                               
                          AMERICAN EXPLORATION COMPANY                         
             (Exact Name of Registrant as Specified in Its Charter)            
                                                                               
<TABLE>                                                                        
         <S>                                          <C>                         
                         DELAWARE                        74-2086890                               
               (State or Other Jurisdiction of        (I.R.S. Employer                         
               Incorporation or Organization)         Identification No.)                         
                                                                               
                                                                               
               1331 LAMAR, SUITE 900                                           
                    HOUSTON, TEXAS                          77010                   
         (Address of Principal Executive Offices)        (Zip Code)                      
</TABLE>                                                                       
                                                                               
                                                                               
      REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE:  (713) 756-6000     
                                                                               
         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  / /                 
                                                                               
         ON OCTOBER 15, 1996, THERE WERE OUTSTANDING 11,807,741 SHARES OF THE  
REGISTRANT'S COMMON STOCK, PAR VALUE $0.05 PER SHARE.                          
                                                                               
================================================================================
                                                                   
                                                                    
<PAGE>   2
                                                                               
                 AMERICAN EXPLORATION COMPANY AND SUBSIDIARIES                 
                         Quarterly Report on Form 10-Q                         
                    for the Quarter Ended September 30, 1996                   
                                                                               
                                  (Unaudited)                                  
                                                                               
<TABLE>                                                             
<CAPTION>                                                                                                       
                                                                                                        Page    
                                                                                                        Number  
                                                                                                      ----------
<S>                                                                                                       <C>   
PART I.   FINANCIAL INFORMATION                                                                                 
                                                                                                                
   Item 1.    Financial Statements                                                                              
                                                                                                                
              Condensed Consolidated Balance Sheets as of September 30, 1996 and                                
                 December 31, 1995  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1    
                                                                                                                
              Condensed Consolidated Statements of Operations for the Three Months                              
                 Ended September 30, 1996 and 1995 and the Nine Months Ended                                    
                 September 30, 1996 and 1995  . . . . . . . . . . . . . . . . . . . . . . . . . .          2    
                                                                                                                
              Condensed Consolidated Statements of Cash Flows for the Nine Months                               
                 Ended September 30, 1996 and 1995  . . . . . . . . . . . . . . . . . . . . . . .          3    
                                                                                                                
              Notes to Condensed Consolidated Financial Statements  . . . . . . . . . . . . . . .          4    
                                                                                                                
   Item 2.    Management's Discussion and Analysis of Financial Condition and                                   
                 Results of Operations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          7    
                                                                                                                
PART II.   OTHER INFORMATION                                                                                    
                                                                                                                
   Item 6.    Exhibits and Reports on Form 8-K  . . . . . . . . . . . . . . . . . . . . . . . . .         11    
                                                                                                                
SIGNATURES      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         12    
</TABLE>                                                      
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
<PAGE>   3

                 AMERICAN EXPLORATION COMPANY AND SUBSIDIARIES
                     CONDENSED CONSOLIDATED BALANCE SHEETS
                    (In thousands, except for share amounts)

<TABLE>
<CAPTION>
                                                                             September 30,          December 31,
                                                                                1996                  1995      
                                                                           ---------------        --------------
                                                                             (Unaudited)
<S>                                                                        <C>                    <C>
                                         ASSETS

Current assets:
   Cash and temporary cash investments  . . . . . . . . . . . . . . .      $         6,780        $        7,496
   Accounts receivable  . . . . . . . . . . . . . . . . . . . . . . .               11,203                14,520
   Receivable from partnerships . . . . . . . . . . . . . . . . . . .                -                       429
   Assets held for sale . . . . . . . . . . . . . . . . . . . . . . .               14,384                 -
   Other current assets . . . . . . . . . . . . . . . . . . . . . . .                2,158                   966
                                                                           ---------------        --------------
      Total current assets  . . . . . . . . . . . . . . . . . . . . .               34,525                23,411
                                                                           ---------------        --------------

Property, plant and equipment:
   Oil and gas properties, based on successful efforts accounting . .              337,881               292,027
   Other property and equipment . . . . . . . . . . . . . . . . . . .               13,365                13,036
                                                                           ---------------        --------------
                                                                                   351,246               305,063
   Less:   Accumulated depreciation, depletion and amortization . . .              155,396               154,646
                                                                           ---------------        --------------
      Property, plant and equipment, net  . . . . . . . . . . . . . .              195,850               150,417
                                                                           ---------------        --------------
Other assets  . . . . . . . . . . . . . . . . . . . . . . . . . . . .                2,988                 2,202
                                                                           ---------------        --------------
          Total assets  . . . . . . . . . . . . . . . . . . . . . . .      $       233,363        $      176,030
                                                                           ===============        ==============

               LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
   Accounts payable . . . . . . . . . . . . . . . . . . . . . . . . .      $        15,670        $       18,149
   Payable to partnerships  . . . . . . . . . . . . . . . . . . . . .                1,678                 -
   Accrued liabilities  . . . . . . . . . . . . . . . . . . . . . . .               18,800                16,953
                                                                           ---------------        --------------
      Total current liabilities . . . . . . . . . . . . . . . . . . .               36,148                35,102
                                                                           ---------------        --------------
Long-term debt  . . . . . . . . . . . . . . . . . . . . . . . . . . .              105,000                40,000
                                                                           ---------------        --------------
Other liabilities . . . . . . . . . . . . . . . . . . . . . . . . . .                4,709                 6,448
                                                                           ---------------        --------------

Stockholders' equity:
   Convertible preferred stock, $1.00 par value; 4,000 shares
      issued and outstanding (1996 and 1995)  . . . . . . . . . . . .                    4                     4
   Common stock, $.05 par value; 11,807,741 shares
      issued and outstanding (1996); 11,812,483 shares issued and
      outstanding (1995)  . . . . . . . . . . . . . . . . . . . . . .                  590                   591
   Additional paid-in capital . . . . . . . . . . . . . . . . . . . .              276,658               276,713
   Accumulated deficit  . . . . . . . . . . . . . . . . . . . . . . .             (189,664)             (182,543)
   Unearned compensation  . . . . . . . . . . . . . . . . . . . . . .                  (79)                 (219)
   Notes receivable from officers . . . . . . . . . . . . . . . . . .                   (3)                  (66)
                                                                           ---------------        -------------- 
      Total stockholders' equity  . . . . . . . . . . . . . . . . . .               87,506                94,480
                                                                           ---------------        --------------
          Total liabilities and stockholders' equity  . . . . . . . .      $       233,363        $      176,030
                                                                           ===============        ==============
</TABLE>

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




                                      1
<PAGE>   4
                 AMERICAN EXPLORATION COMPANY AND SUBSIDIARIES
                CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                  (In thousands, except for per share amounts)
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                 For the Three Months      For the Nine Months
                                                                 Ended September 30,       Ended September 30,
                                                                ----------------------    ----------------------
                                                                  1996         1995         1996         1995   
                                                                ---------    ---------    ---------    ---------
<S>                                                             <C>          <C>          <C>          <C>
REVENUES:
   Oil and gas sales  . . . . . . . . . . . . . . . . . .       $  19,090    $  16,890    $  52,263    $  55,049
   Gain on sales of oil and gas properties  . . . . . . .             145        9,231          801        9,674
   Other revenues (costs), net  . . . . . . . . . . . . .              84         (282)         111          678
                                                                ---------    ---------    ---------    ---------
      Total revenues  . . . . . . . . . . . . . . . . . .          19,319       25,839       53,175       65,401
                                                                ---------    ---------    ---------    ---------

COSTS AND EXPENSES:
   Production and operating . . . . . . . . . . . . . . .           5,225        5,555       15,421       19,079
   Depreciation, depletion and amortization . . . . . . .           7,398        6,894       20,871       22,446
   General and administrative . . . . . . . . . . . . . .           1,267        1,700        4,450        4,683
   Taxes other than income  . . . . . . . . . . . . . . .           1,638        1,275        4,254        4,413
   Exploration  . . . . . . . . . . . . . . . . . . . . .           2,001        3,109        9,152        3,269
   Impairment . . . . . . . . . . . . . . . . . . . . . .           1,841           43        1,841           43
                                                                ---------    ---------    ---------    ---------
      Total costs and expenses  . . . . . . . . . . . . .          19,370       18,576       55,989       53,933
                                                                ---------    ---------    ---------    ---------
INCOME (LOSS) FROM OPERATIONS . . . . . . . . . . . . . .             (51)       7,263       (2,814)      11,468
                                                                ---------    ---------    ---------    ---------
OTHER INCOME (EXPENSE):
   Interest expense . . . . . . . . . . . . . . . . . . .          (1,076)      (1,002)      (2,894)      (4,853)
   Other expense, net . . . . . . . . . . . . . . . . . .            (117)        (246)         (63)        (105)
                                                                ---------    ---------    ---------    --------- 
      Total other expense . . . . . . . . . . . . . . . .          (1,193)      (1,248)      (2,957)      (4,958)
                                                                ---------    ---------    ---------    --------- 
INCOME (LOSS) BEFORE EXTRAORDINARY ITEM . . . . . . . . .          (1,244)       6,015       (5,771)       6,510

Extraordinary gain on extinguishment of debt  . . . . . .           -            -            -            2,456
                                                                ---------    ---------    ---------    ---------
NET INCOME (LOSS) . . . . . . . . . . . . . . . . . . . .          (1,244)       6,015       (5,771)       8,966

Preferred stock dividends . . . . . . . . . . . . . . . .            (450)        (450)      (1,350)      (1,350)
                                                                ---------    ---------    ---------    --------- 
NET INCOME (LOSS) TO COMMON STOCK . . . . . . . . . . . .       $  (1,694)   $   5,565    $  (7,121)   $   7,616
                                                                =========    =========    =========    =========

NET INCOME (LOSS) PER COMMON SHARE:
   Primary and fully diluted:
      Income (loss) before extraordinary item . . . . . .       $   (0.14)   $    0.47    $   (0.60)   $    0.43
      Extraordinary item  . . . . . . . . . . . . . . . .           -            -            -             0.21
                                                                ---------    ---------    ---------    ---------
         NET INCOME (LOSS) PER COMMON SHARE . . . . . . .       $   (0.14)   $    0.47    $   (0.60)   $    0.64
                                                                =========    =========    =========    =========

NUMBER OF COMMON AND EQUIVALENT SHARES:
   Primary and fully diluted  . . . . . . . . . . . . . .          11,808       11,814       11,811       11,812
                                                                =========    =========    =========    =========
</TABLE>


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





                                       2
<PAGE>   5
                 AMERICAN EXPLORATION COMPANY AND SUBSIDIARIES
                CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (In thousands)
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                                      For the Nine Months
                                                                                      Ended September 30,      
                                                                                  ------------------------------
                                                                                      1996              1995
                                                                                  ------------      ------------
<S>                                                                               <C>               <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income (loss)  . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $     (5,771)     $      8,966
   Adjustments to arrive at net cash provided by operating activities:
      Depreciation, depletion and amortization  . . . . . . . . . . . . . . .           20,871            22,446
      Gain on sales of oil and gas properties . . . . . . . . . . . . . . . .             (801)           (9,674)
      Exploration expense . . . . . . . . . . . . . . . . . . . . . . . . . .            9,152             3,208
      Impairment expense  . . . . . . . . . . . . . . . . . . . . . . . . . .            1,841                43
      Extraordinary gain on extinguishment of debt  . . . . . . . . . . . . .            -                (2,456)
      Other, net  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .              343               531
   Changes in operating working capital:
      Accounts receivable . . . . . . . . . . . . . . . . . . . . . . . . . .            5,216            (1,971)
      Other current assets  . . . . . . . . . . . . . . . . . . . . . . . . .              214              (472)
      Accounts payable and accrued liabilities  . . . . . . . . . . . . . . .           (3,053)            2,457
   Other operating  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             (903)              659
                                                                                  ------------      ------------
      NET CASH PROVIDED BY OPERATING ACTIVITIES . . . . . . . . . . . . . . .           27,109            23,737
                                                                                  ------------      ------------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Acquisition of oil and gas properties  . . . . . . . . . . . . . . . . . .          (62,832)          (11,087)
   Development and exploration expenditures . . . . . . . . . . . . . . . . .          (29,284)          (20,142)
   Proceeds from sales of oil and gas properties, net . . . . . . . . . . . .            1,194            62,218
   Other investing  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             (415)            1,585
                                                                                  ------------      ------------
      NET CASH PROVIDED BY (USED IN) INVESTING ACTIVITIES . . . . . . . . . .          (91,337)           32,574
                                                                                  ------------      ------------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Bank debt borrowings . . . . . . . . . . . . . . . . . . . . . . . . . . .           74,000            43,500
   Bank debt repayments . . . . . . . . . . . . . . . . . . . . . . . . . . .           (9,000)          (69,500)
   Repayments under bridge credit facility  . . . . . . . . . . . . . . . . .            -               (31,128)
   Preferred stock dividends  . . . . . . . . . . . . . . . . . . . . . . . .           (1,350)           (1,350)
   Other financing  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             (138)           (1,363)
                                                                                  ------------      ------------ 
      NET CASH PROVIDED BY (USED IN) FINANCING ACTIVITIES . . . . . . . . . .           63,512           (59,841)
                                                                                  ------------      ------------ 
NET DECREASE IN CASH AND TEMPORARY CASH INVESTMENTS . . . . . . . . . . . . .             (716)           (3,530)

CASH AND TEMPORARY CASH INVESTMENTS AT BEGINNING OF PERIOD  . . . . . . . . .            7,496             9,973
                                                                                  ------------      ------------
CASH AND TEMPORARY CASH INVESTMENTS AT END OF PERIOD  . . . . . . . . . . . .     $      6,780      $      6,443
                                                                                  ============      ============
</TABLE>


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





                                       3
<PAGE>   6
                 AMERICAN EXPLORATION COMPANY AND SUBSIDIARIES
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                  (Unaudited)


(1)   BASIS OF PRESENTATION

   The condensed consolidated financial statements included herein have been
prepared by American Exploration Company ("American" or the "Company"), without
audit, pursuant to the rules and regulations of the Securities and Exchange
Commission (the "Commission").  The financial statements reflect adjustments of
a normal recurring nature which are, in the opinion of management, necessary to
present fairly such information.  Although the Company believes that the
disclosures are adequate to make the information presented not misleading,
certain information and footnote disclosures, including significant accounting
policies, normally included in financial statements prepared in accordance with
generally accepted accounting principles have been condensed or omitted
pursuant to such rules and regulations.  It is suggested that these condensed
consolidated financial statements be read in conjunction with the financial
statements and the notes thereto included in the Company's Annual Report on
Form 10-K for the year ended December 31, 1995.  Certain amounts in the prior
year financial statements have been reclassified to conform with current
classifications.

   The Company effected a one-for-ten reverse split of its common stock (the
"Reverse Stock Split") during the second quarter of 1995.  All references to
numbers of shares of common stock and per share amounts have been restated to
give retroactive recognition to the Reverse Stock Split for all periods
presented.

(2)   ACQUISITION OF OIL AND GAS PROPERTIES

   On September 27, 1996, the Company acquired interests in two blocks in the
Gulf of Mexico, High Island Block 116 and East Cameron Block 328, for a
purchase price of approximately $39 million, net of interests being sold to a
third party (the "September 1996 Acquisition").  The September 1996 Acquisition
was funded through borrowings under the Company's revolving bank credit
agreement (the "Credit Agreement").

(3)   ASSETS HELD FOR SALE

   In July 1996, the limited partners of the New York Life Oil and Gas
Producing Properties Programs (the "NYLOG Programs"), a series of publicly
registered limited partnerships of which a Company subsidiary is a co-general
partner, approved the liquidation of the partnerships.  The Company is in the
process of selling interests in approximately 70 properties, including those
properties owned by the NYLOG Programs and certain related properties (the
"1996 Sales"), and expects to complete the sales by year-end 1996.  The
Company's interests in the properties that are expected to be sold in the 1996
Sales have been classified as assets held for sale in the accompanying balance
sheet as of September 30, 1996.  Although there can be no assurance as to the
amount of proceeds to be derived from such sales, the Company believes that the
net proceeds from the property dispositions will exceed the current carrying
value of the properties.  Accordingly, the assets held for sale are stated at
net book value.

   Assets held for sale also include certain interests in High Island Block 116
that were acquired by the Company in the September 1996 Acquisition and that
are expected to be sold to a third party during the fourth quarter of 1996.
Oil and gas production and reserves data for the September 1996 Acquisition
presented in this report do not include any amounts attributable to the
interests expected to be sold.

(4)   PRO FORMA INFORMATION

   The following pro forma summary of consolidated results of operations for
the nine months ended September 30, 1996 and 1995 gives effect to:  (i) that
portion of the acquisition of investors' interests in a series of institutional
programs (the "APPL Consolidation"), which was completed in the first half of
1995 for a purchase price of approximately $9 million, (ii) the sale of the
Company's interest in the Sawyer Field in July 1995 for proceeds of
approximately $64 million (the "Sawyer Sale"), (iii) the 1995 sales of
interests in several other fields for approximately $2.5 million, (iv) the




                                      4
<PAGE>   7
acquisition by the Company of interests in five offshore blocks in the Gulf of
Mexico in March 1996 for a purchase price of approximately $14 million (the
"March 1996 Acquisition"), (v) the September 1996 Acquisition and (vi) the 1996
Sales, as if these transactions had occurred as of January 1, 1995.

   The pro forma results for the nine-month period of 1996 include only two
months of results from the High Island 116 well acquired in the September 1996
Acquisition, and the pro forma results for the nine-month period of 1995 do not
include any results from that well because the well did not produce during the
applicable period.  The well commenced production in August 1996 at a net
production rate of approximately 300 Bbls of oil per day and approximately
17,100 Mcf of natural gas per day.  Similarly, the 1995 pro forma results
include only seven months of results from the East Cameron 328 well, also
purchased in the September 1996 Acquisition, which commenced production in
March 1995.  In addition, the 1995 pro forma results have been adjusted to
eliminate the nonrecurring gain on the Sawyer Sale of approximately $10
million.

<TABLE>
<CAPTION>
(In thousands except for per share amounts)                                            For the Nine Months
                                                                                       Ended September 30,       
                                                                                 -------------------------------
                                                                                    1996               1995     
                                                                                 ------------       ------------
<S>                                                                              <C>                <C>
Pro forma revenues  . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $     53,840       $     48,950
Pro forma loss before extraordinary item  . . . . . . . . . . . . . . . . .            (9,027)            (5,303)
Pro forma net loss to common stock  . . . . . . . . . . . . . . . . . . . .            (9,027)            (2,847)
Pro forma net loss per common share:
   Primary and fully diluted:
      Loss before extraordinary item  . . . . . . . . . . . . . . . . . . .      $      (0.76)      $      (0.45)
      Net loss  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             (0.76)             (0.24)
   Weighted average shares outstanding:
      Primary and fully diluted . . . . . . . . . . . . . . . . . . . . . .            11,811             11,812
</TABLE>

   The pro forma amounts do not purport to be indicative of the results of
operations of American that may be reported in the future or that would have
been reported had these transactions occurred as of January 1, 1995.

(5)   DEBT

   Outstanding bank debt totaled $70 million as of September 30, 1996.  The
Company borrowed approximately $14 million under the Credit Agreement to fund
the March 1996 Acquisition.  American borrowed $45 million to fund the
September 1996 Acquisition, which amount was the purchase price before
considering the interests to be sold to a third party.

   As of September 30, 1996, the borrowing base under the Credit Agreement was
$90 million, reflecting the increase in the aggregate value of the Company's
oil and gas properties due to the March 1996 Acquisition and the September 1996
Acquisition.  The Company has filed a registration statement with the
Commission regarding the proposed sale by the Company of 3,000,000 shares of
the Company's common stock for estimated net proceeds of approximately $33.8
million.  If the common stock offering is completed and the net proceeds are
applied to reduce bank debt, the Company anticipates that the amount
outstanding under the Credit Agreement will be approximately $21.8 million and
the borrowing base will be approximately $75 million.  The borrowing base is
scheduled to be redetermined semi-annually every March and September.

   Under the terms of an amendment to the Credit Agreement dated October 15,
1996, principal payments under the Credit Agreement are scheduled to be repaid
in ten quarterly installments commencing September 30, 1999.  Principal
payments under the Credit Agreement had previously been scheduled to begin in
September 1997.




                                      5
<PAGE>   8
   In September 1996, holders of the Company's 11% senior subordinated notes
(the "Subordinated Notes") agreed to an extension of the principal payment
dates of the notes, which were scheduled to begin in December 1997, in exchange
for a reduction in the exercise price, from $22.95 per share to $15.53 per
share, of warrants to purchase shares of the Company's common stock that were
issued to the holders of the notes contemporaneously with the issuance of such
notes.  As a result of this extension, annual principal payments of
approximately $11.7 million on the Subordinated Notes will begin in December
2002.

(6)   CASH FLOW INFORMATION

   Net cash provided by operating activities included cash payments for
interest totaling $1.9 million and $4.1 million, net of capitalized interest of
$1.5 million and $1.0 million, for the first nine months of 1996 and 1995,
respectively.  No income taxes were paid by the Company in the first nine
months of 1996.  The Company paid income taxes of $47,000 for the first nine
months of 1995.

   Noncash investing and financing activities in 1995 related to the APPL
Consolidation.  In January 1995, American issued approximately 346,000 shares
of common stock valued at $12.50 per share to acquire $1.2 million of oil and
gas properties, including working capital, and to eliminate $4.7 million of
nonrecourse debt, resulting in an extraordinary gain of $1.6 million.




                                      6
<PAGE>   9
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
         RESULTS OF OPERATIONS

RESULTS OF OPERATIONS

   The following table sets forth certain operating information of the Company
for the periods presented in the accompanying financial statements.

<TABLE>
<CAPTION>
                                                                  For the Three Months      For the Nine Months
                                                                  Ended September 30,       Ended September 30,
                                                                ----------------------    ----------------------
                                                                  1996         1995         1996         1995   
                                                                ---------    ---------    ---------    ---------
<S>                                                             <C>          <C>          <C>          <C>
Average Sales Price (1):
------------------------
   Gas ($/Mcf)  . . . . . . . . . . . . . . . . . . . . .       $    1.90    $    1.69    $    1.88    $    1.70
   Oil ($/Bbl)  . . . . . . . . . . . . . . . . . . . . .           17.20        16.64        16.87        16.87
   BOE ($/BOE)  . . . . . . . . . . . . . . . . . . . . .           13.23        12.02        13.17        12.05

Production Data:
----------------
   Gas (MMcf) . . . . . . . . . . . . . . . . . . . . . .           5,942        6,013       15,772       19,866
   Oil (MBbls)  . . . . . . . . . . . . . . . . . . . . .             453          403        1,340        1,258
   MBOE . . . . . . . . . . . . . . . . . . . . . . . . .           1,443        1,405        3,969        4,569

Additional Data ($/BOE):
------------------------
   Production and operating costs . . . . . . . . . . . .       $    3.62    $    3.95    $    3.89    $    4.18
   General and administrative expense . . . . . . . . . .            0.88         1.21         1.12         1.02
   Taxes other than income  . . . . . . . . . . . . . . .            1.13         0.91         1.07         0.97
   Depreciation, depletion and amortization . . . . . . .            5.13         4.91         5.26         4.91
</TABLE>

_________________
(1)Prices reflect impact of hedging gains and losses.


REVENUES

   The Company recorded oil and gas sales of $19.1 million for the third
quarter of 1996 compared to $16.9 million for the third quarter of 1995.
Higher sales for the third quarter of 1996 primarily reflect a 12% increase in
the Company's average gas price and increased oil production relative to the
third quarter of 1995.  For the first nine months of the year, oil and gas
sales totaled $52.3 million in 1996 and $55 million in 1995.  The decline in
sales for the year-to-date period of 1996, compared to the same period of
1995, is mainly attributable to the Sawyer Sale, offset in part by higher gas
prices and increased oil production.

   Gas production for the third quarter of 1996 totaled 5,942 MMcf,
representing a 1% decline from third quarter 1995 production of 6,013 MMcf.
Gas production from the properties acquired in the March 1996 Acquisition,
together with higher production due to successful development activity at High
Island Block 13-L and the Bradshaw Field, more than offset the decrease of
approximately 700 MMcf of July 1995 production from the Sawyer Field included
in the third quarter 1995 results.  For the nine months ended September 30,
1996, gas production totaled 15,772 MMcf compared to 19,866 MMcf for the same
period of 1995.  The production decline for the year-to-date period reflected
the loss of production of approximately 20 MMcf per day due to the Sawyer Sale.
For the quarterly and year-to-date periods, the decline in gas volumes in 1996
negatively impacted sales by approximately $100,000 and approximately $6.9
million, respectively.

   Oil production for the third quarter of 1996 increased to 453 MBbls from 403
MBbls for the third quarter of 1995 primarily due to additional volumes related
to the March 1996 Acquisition.  On a year-to-date basis, oil production
increased to a lesser extent, totaling 1,340 MBbls for the first nine months of
1996, or 7% above the same period of 1995.  Year-to-date production increases
resulting from the March 1996 Acquisition, the late 1995 acquisition of an
additional interest in the Buckner Field and the successful 1995 drilling
program at the Midway Field were partially offset by the impact of the sales of
several oil producing properties in late 1995 and early 1996.  Increased oil
production contributed approximately $800,000 to the Company's third quarter
revenues in 1996 and approximately $1.4 million to year-to-date 1996 revenues.




                                      7
<PAGE>   10
   The Company's 1996 revenues were favorably impacted by approximately $1.5
million due to the effect of higher oil and gas prices in the third quarter of
1996 and by approximately $2.8 million due to higher gas prices for the first
nine months of 1996, compared to the respective periods of 1995.  American's
gas price averaged $1.90 per Mcf and $1.88 per Mcf for the quarterly and
nine-month periods of 1996, respectively, compared to $1.69 per Mcf for the
third quarter of 1995 and $1.70 per Mcf for the first nine months of 1995.  The
Company's average oil price increased by 3% for the quarterly period, rising to
$17.20 per Bbl in the third quarter of 1996 from $16.64 per Bbl for the same
period of 1995.  For the first nine months of the year, American recorded an
average oil price of $16.87 per Bbl in both 1996 and 1995.

   During the third quarter of 1996, the Company had in effect commodity price
swap agreements covering approximately 36% of American's gas production and
approximately 69% of its oil production.  As a result of the price hedges, the
Company's oil and gas sales revenues were reduced by approximately $2.3 million
during the third quarter of 1996 and were increased by approximately $1.4
million during the same period of 1995.  Excluding the impact of the hedging
gains and losses, American's average oil and gas prices for the third quarter
of 1996 would have been $20.47 per Bbl and $2.04 per Mcf.  For the third
quarter of 1995, the Company's average prices exclusive of the hedges would
have been $15.93 per Bbl and $1.51 per Mcf.

   For the first nine months of 1996, hedging agreements covered approximately
52% of the Company's gas production and approximately 67% of its oil
production, resulting in a revenue reduction of approximately $6.1 million.
American's year-to-date 1996 oil and gas prices would have averaged $19.39 per
Bbl and $2.05 per Mcf exclusive of the hedges.  For the comparable period of
1995, the Company recorded a net hedging gain of approximately $2 million.  The
Company's average gas price for the first nine months of 1995 was increased by
$0.10 per Mcf due to the hedges while the average oil price was reduced by
$0.07 per Bbl.

   In September 1996, the Company entered into additional commodity price swap
agreements covering 3,000 barrels of daily oil production for the period from
January 1, 1997 through December 31, 1997 at an average fixed price of $19.48
per Bbl.  For information regarding oil and gas price hedging arrangements in
effect for the remainder of 1996, reference is made to the Company's Annual
Report on Form 10-K for the fiscal year ended December 31, 1995.

   During the third quarter of 1995, American reported a gain on the Sawyer
Sale of approximately $10 million.  Also in 1995, other revenues for the
nine-month period included $879,000 of net gas settlement income as a result of
the final judgment in certain litigation regarding the terms of a gas purchase
contract.

COSTS AND EXPENSES

   Production and operating costs totaled $5.2 million, or $3.62 per BOE, for
the third quarter of 1996 and $5.6 million, or $3.95 per BOE, for the third
quarter of 1995.  The 6% decrease in production costs resulted from reduced
production in the third quarter of 1996 while the decline in the Company's
operating cost per unit of production was mainly attributable to the impact of
the offshore properties acquired in the March 1996 Acquisition.  Such
properties have high production volumes and low operating costs relative to the
Company's onshore properties.  For the nine-month period, production and
operating costs decreased to $15.4 million, or $3.89 per BOE, in 1996 from
$19.1 million, or $4.18 per BOE, in 1995.  The reduction in total costs was
primarily attributable to the Sawyer Sale, while lower unit costs mainly
reflected the impact of the March 1996 Acquisition.

   Depreciation, depletion and amortization ("DD&A") totaled $7.4 million and
$6.9 million for the third quarter of 1996 and 1995, respectively.  The
increase in DD&A for the quarterly periods primarily reflected the higher
depletion rates associated with platform abandonment costs for the offshore
properties in the Gulf of Mexico, which represent a greater portion of the
Company's property base than in 1995.  For the year-to-date period, DD&A
totaled $20.9 million in 1996 and $22.4 million in 1995.  DD&A for the
nine-month period declined in 1996 due to lower gas production volumes
resulting from the Sawyer Sale, with that decline partially offset by the
impact of higher depletion rates on the offshore properties.

   General and administrative ("G&A") expense declined to $1.3 million for the
third quarter of 1996 from $1.7 million for the same period of 1995.  The
reduction in G&A expense reflected lower legal fees in 1996 as the 1995 quarter
included certain costs to resolve a dispute involving a well owned by one of
the NYLOG partnerships.  For the first nine months of 1996, G&A expense totaled
$4.5 million compared to $4.7 million for the same period of 1995.




                                      8
<PAGE>   11
   Taxes other than income totaled $1.6 million and $1.3 million for the third
quarter of 1996 and 1995, respectively.  Production tax expense for the 1995
quarter was unusually low due to the impact of certain severance tax refunds
received related to an outside operated property.  During the first nine months
of the year, taxes other than income totaled $4.3 million in 1996 and $4.4
million in 1995.  On a year-to-date basis, the reduction in production taxes in
1996 due to the Sawyer Sale was essentially offset by the impact of the
severance tax refunds received in 1995, as mentioned above, and higher ad
valorem taxes in 1996.

   Exploration expense totaled $2 million and $3.1 million for the third
quarter of 1996 and 1995, respectively, and totaled $9.2 million and $3.3
million for the first nine months of 1996 and 1995, respectively.  The Company
began to shift its focus towards exploration activity in late 1995.  For the
year-to-date 1996 period, exploration expense included the costs of eleven
unsuccessful exploratory wells which were primarily offshore in the Gulf of
Mexico.  Impairment expense of $1.8 million in the third quarter of 1996
related to the write-off of unproved properties on which no further exploration
or development activity is planned.

   Interest expense for the third quarter of 1996 totaled $1.1 million compared
to $1 million for the same period of 1995.  In addition to interest on the
Subordinated Notes, interest expense for the 1996 quarter related to the
Company's average outstanding bank debt of approximately $25 million for
substantially all of the third quarter of 1996 (since the $45 million funding
of the September 1996 Acquisition occurred near the end of the quarter) while
such expense for the 1995 quarter was primarily based on a $62.5 million bank
debt balance which was outstanding for only one month of the quarter before
being eliminated by the application of the proceeds from the Sawyer Sale.  For
the first nine months of 1996, interest expense of $2.9 million was 40% below
the same period in 1995 reflecting higher bank debt carried in the first half
of 1995 following the completion of the APPL Consolidation.

EXTRAORDINARY ITEM

   The $2.5 million extraordinary gain recorded in 1995 resulted from the
extinguishment of nonrecourse debt in conjunction with the APPL Consolidation.

NET INCOME (LOSS)

   The Company reported a net loss of $1.2 million and $5.8 million for the
third quarter and first nine months of 1996, respectively, compared to net
income of $6 million for the third quarter of 1995 and net income of $9 million
for the year-to-date period of 1995.  Net losses during 1996 were attributable
to an aggregate charge of $3.8 million for exploration and impairment expenses
for the third quarter and $11 million of such expenses for the first nine
months of the year.  In 1995, net income for both periods included the impact
of an approximate $10 million gain on the Sawyer Sale, and year-to-date 1995
income also reflected a $2.5 million extraordinary gain on debt extinguishment.

CAPITAL RESOURCES AND LIQUIDITY

   The Company's principal sources of capital are net cash provided by
operating activities and proceeds from financing activities.  During the last
three years, the Company has also generated substantial cash flows from the
sale of oil and gas properties, most notably the Sawyer Sale.  The Company's
primary uses of capital are to fund its development and exploration programs
and acquisition activity.  The Company also has financial obligations related
to its preferred stock and Subordinated Notes.

   Net cash provided by operating activities totaled $27.1 million during the
first nine months of 1996 compared to $23.7 million during the same period of
1995.  The improvement in operating cash flows was attributable to a higher
operating margin per unit of production in 1996 resulting from higher gas
prices, reduced production and operating costs and lower interest expense.

   On September 30, 1996, the Company filed a registration statement with the
Commission regarding the proposed sale of 3,579,229 shares of the Company's
common stock.  Of the shares to be sold, 3,000,000 shares are being offered by
the Company, and the remaining shares are being sold by certain shareholders
pursuant to certain registration rights previously granted by American.  The
net proceeds to the Company from the sale of the 3,000,000 shares (the
"Offering") are estimated to be approximately $33.8 million.  These net
proceeds will be used to reduce outstanding indebtedness under




                                      9
<PAGE>   12
the Credit Agreement, as discussed below.  The Company will not receive any
proceeds from the sale of shares by the other shareholders.

   Outstanding bank debt totaled $70 million as of September 30, 1996.  The
Company borrowed approximately $14 million under the Credit Agreement to fund
the March 1996 Acquisition.  American borrowed $45 million to fund the
September 1996 Acquisition, which amount was the purchase price before
considering the interests to be sold to a third party.

   As of September 30, 1996, the borrowing base under the Credit Agreement was
$90 million, reflecting the increase in the aggregate value of the Company's
oil and gas properties due to the March 1996 Acquisition and the September 1996
Acquisition.  If the Offering is completed and the net proceeds are applied to
reduce bank debt, the Company anticipates that the amount outstanding under the
Credit Agreement will be approximately $21.8 million and the borrowing base
will be approximately $75 million.  The borrowing base is scheduled to be
redetermined semi-annually every March and September.

   Under the terms of an amendment to the Credit Agreement dated October 15,
1996, principal payments under the Credit Agreement are scheduled to be repaid
in ten quarterly installments commencing September 30, 1999.  Principal
payments under the Credit Agreement had previously been scheduled to begin in
September 1997.

   In September 1996, holders of the Subordinated Notes agreed to an extension
of the principal payment dates of the notes, which were scheduled to begin in
December 1997, in exchange for a reduction in the exercise price, from $22.95
per share to $15.53 per share, of warrants to purchase shares of the Company's
common stock that were issued to the holders of the notes contemporaneously
with the issuance of such notes.  As a result of this extension, annual
principal payments of approximately $11.7 million on the Subordinated Notes
will begin in December 2002.

   During the first nine months of 1996, capital expenditures for the
acquisition of oil and gas properties totaled $62.8 million, compared to $11.1
million for the same period of 1995.  Through September 30, 1996, the Company
invested $53 million, net of interests being sold to a third party, to acquire
interests in seven blocks in the Gulf of Mexico, four of which are operated by
the Company.  In aggregate, the March 1996 Acquisition and the September 1996
Acquisition added estimated proved reserves of approximately 4.2 MMBbls of oil
and 28.2 Bcf of natural gas (as estimated by the Company as of the date of each
acquisition).  Other acquisition expenditures in 1996 primarily related to
leasehold additions in South Texas and the Gulf of Mexico.  Acquisition
expenditures in 1995 primarily related to the APPL Consolidation.

   Development and exploration expenditures for the first nine months of 1996
and 1995 totaled $29.3 million and $20.1 million, respectively.  Significant
development activity in 1996 included a successful well at High Island Block
13-L and eleven completions at the Bradshaw Field in Kansas.  The Company is
conducting additional development activity in the Gulf of Mexico and in various
fields in South Texas.  The Company participated in the completion of 16
exploratory wells during the first nine months of 1996, of which five wells
were successful, including four prospects in South Texas.  Through September
1996, the Company participated in 50 gross wells (18.7 net), with a success
rate of approximately 70%.  The Company plans to invest approximately $15
million and to drill over 20 wells during the fourth quarter of 1996.  There
can be no assurances regarding the success of any wells drilled, and
exploratory wells involve greater risks than development wells.  Under
successful efforts accounting, the costs incurred for the drilling of
unsuccessful exploratory wells are recorded as exploration expense which would
negatively impact net income in the period in which incurred.

   The Company expects its 1997 capital expenditures for development and
exploration activities to range from $50 million to $75 million depending on
various factors, including the level of exploration success and subsequent
development activity.  Following the Offering, the Company intends to fund its
planned capital expenditures, commitments and working capital requirements
through cash flows from operations and, if necessary, borrowings under the
Credit Agreement.  However, if there are changes in oil and gas prices, which
correspondingly affect cash flows and bank borrowings, or if additional
development and exploration opportunities arise, American has the discretion
and ability to adjust its capital budget accordingly.  Other potential sources
of capital for the Company include property sales and financings through the
placement of notes or the sale of equity.  Management believes that the Company
will have sufficient capital resources and liquidity to fund its capital
expenditures and meet its financial obligations as they are due.

   As a result of the Offering, the Company will be subject to revised
individual annual and cumulative net operating loss carryforward ("NOL") limits
for federal income tax purposes.  Prior to the Offering, the Company's annual
and




                                      10
<PAGE>   13
cumulative NOL limits totaled approximately $13.7 million and approximately
$76.3 million, respectively.  Upon completion of the Offering, the Company's
annual and cumulative NOL limits will each be approximately $10 million due to
changes in the Company's ownership over the last three years.

                                    PART II

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

   (a)   Exhibits.

         10(a) Amendment No. 6 to Amended and Restated Credit Agreement, dated
               October 15, 1996, among American Exploration Company, the banks
               listed herein and Morgan Guaranty Trust Company of New York, as
               agent, and Bank of Montreal, as co-agent.

         27    Financial Data Schedule.

   (b)   Reports on Form 8-K.

         The Company filed a Current Report on Form 8-K dated September 18,
         1996, reporting the proposed sales of certain interests in oil and gas
         properties and the acquisition of interests in two offshore blocks in
         the Gulf of Mexico.

         On September 30, 1996, the Company amended its Current Report on Form
         8-K, dated March 15, 1996, by filing a Current Report on Form 8-K/A
         which included audited financial statements of certain interests in
         oil and gas properties that were acquired by the Company in March
         1996.




                                      11
<PAGE>   14
                                   SIGNATURES


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


                                       AMERICAN EXPLORATION COMPANY





Date:  October 25, 1996                By:  /s/ MARK ANDREWS
                                            ----------------------------------
                                            Mark Andrews
                                            Chairman of the Board
                                            and Chief Executive Officer
       
       
       
       
       
Date:  October 25, 1996                By:  /s/ JOHN M. HOGAN
                                            ----------------------------------
                                            John M. Hogan
                                            Senior Vice President
                                            and Chief Financial Officer
                                            (Also Principal Accounting Officer)
       
       
       

                                      12
                                       
                                       
<PAGE>   15
                                EXHIBIT INDEX

         10(a) Amendment No. 6 to Amended and Restated Credit Agreement, dated
               October 15, 1996, among American Exploration Company, the banks
               listed herein and Morgan Guaranty Trust Company of New York, as
               agent, and Bank of Montreal, as co-agent.

         27    Financial Data Schedule.