Two hedge funds holding American Airlines debt lashed out at Chief Executive Tom Horton, saying the airline company is excluding them from discussions on how it should emerge from bankruptcy proceedings while engaging in “inappropriate” talks with another group of bondholders, according to people familiar with the matter.

In a letter to Mr. Horton Thursday, representatives of Appaloosa Management LP and Marathon Asset Management said they together hold more than $800 million of the airline’s debt and that bankruptcy proceedings for American Airlines parent AMR Corp. AAMRQ +1.09% “have not been sufficiently transparent” or “inclusive” to some nonunion creditors who could own significant shares of the company after it reorganizes, said people familiar with the letter.