1
 
   
                                                                   EXHIBIT 23(b)
    
 
   
                        INDEPENDENT ACCOUNTANTS' CONSENT
    
 
   
The Board of Directors
    
   
American Exploration Company:
    
 
   
     We consent to the incorporation by reference in this registration statement
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 31, 1996