The U.S. Federal Appeals Court in Cincinnati heard the case of a retired Ohio autoworker accused of being a Nazi death camp guard.
The Federal Government has been trying to deport John Demjanjuk for 30 years.
Demjanjuk is now 87 and lives in suburban Cleveland.
Thursday's arguments revolved around whether an immigration judge had the authority in 2005 to order Demjanjuk deported to his native Ukraine.
The three judge panel didn't say when it would rule.
