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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. 33-XXXXX) 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
September 26, 1996