A former soldier from Midland is fighting his conviction on rape and murder in Iraq.
Steven Green was tried in a civilian court despite committing the crime while on active duty.
The federal appeals court is looking at the constitutionality of the law that allowed the government to try and convict him in a civilian court.
Green was the first person charged under the law that allows U.S. authorities to prosecute former military personnel, contractors and others for crimes committed overseas.
The Midlander was convicted of raping and killing an Iraqi girl and murdering three of her family members.
He was given five life sentences.