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                                                                   EXHIBIT 23(B)
 
                        INDEPENDENT ACCOUNTANTS' CONSENT
 
The Board of Directors
American Exploration Company:
 
   
     We consent to the inclusion in the registration statement (No. 333-13017)
on Form S-1 of American Exploration Company of our report dated September 26,
1996, relating to the statements of oil and gas revenues and direct lease
operating expenses of the Zilkha I Properties for each of the years in the
three-year period ended December 31, 1995, and to the reference to our firm
under the heading "Experts" in the prospectus.
    
 
                                          KPMG PEAT MARWICK LLP
 
Houston, Texas
   
October 25, 1996