<PAGE>
PROSPECTUS SUPPLEMENT NO. 44, DATED JUNE 7, 1996 PURSUANT TO
- ------------------------------------------------- RULE 424(B)(3)
(TO PROSPECTUS DATED OCTOBER 3, 1994) REG. NO. 33-54561
800,000 DEPOSITARY SHARES,
4,000 SHARES OF $450 CUMULATIVE CONVERTIBLE PREFERRED STOCK
AND
1,777,778 SHARES OF COMMON STOCK
AMERICAN EXPLORATION COMPANY
The following beneficial owner of Depositary Shares has requested the
Company to file a Prospectus Supplement identifying it as a Selling
Securityholder. The information concerning such Selling Securityholder has
been provided by such Selling Securityholder.
<TABLE>
<CAPTION>
NO. OF NO. OF DEPOSITARY % OF OUTSTANDING % OF OUTSTANDING
SELLING DEPOSITARY SHARES DEPOSITARY SHARES DEPOSITARY SHARES
SECURITYHOLDER SHARES OWNED THAT MAY BE SOLD BEFORE SALE AFTER SALE
- -------------- ------------ ---------------- ----------------- -----------------
<S> <C> <C> <C> <C>
Frost-Nevada Limited Partnership
Barnett Banks Trust Company N.A.
701 Brickell Ave
Miami, FL 33131 40,000 40,000 5.00% 0.0%
------ ------ ----- -----
Total 40,000 40,000 5.00% 0.0%
====== ====== ===== =====
</TABLE>
Additional Selling Securityholders or other information concerning the
Selling Securityholder listed above may be set forth in subsequent Prospectus
Supplements from time to time. As a result of such additional Prospectus
Supplements, the total amount of Depositary Shares offered for the account of
Selling Securityholders may increase further, up to a maximum of 800,000
Depositary Shares.
