This is the first time a civilian court is hearing a case former Guantanamo Bay detainee.
A US court of appeals heard arguments in the case of Osama bin Laden's former personal driver, who is challenging his terror conviction even though he has been released.
Salim Hamdan's case marks the first appeal in US civilian court of a former Guantanamo Bay detainee over a conviction issued by the special tribunals known as military commissions.
The court could dismiss the case because Hamdan has served his sentence and is no longer in US custody after he was released in his native Yemen in 2009.
A panel of three judges asked Hamdan's attorneys and US government lawyers to provide a response in writing within two months about whether there is still live controversy surrounding the case.
The hearing room was filled with military and justice officials, including the military commissions' chief prosecutor, Brigadier General Mark Martins, Assistant Attorney General for National Security Lisa Monaco and former solicitor general Neal Katyal.
In the first Guantanamo terror trial, a jury of US military officers sentenced Hamdan to five years and six months for providing material support to Al-Qaeda. Taking into account time served, this amounted to only another five months.
He was cleared of more serious charges that he conspired and plotted attacks for Al-Qaeda.
After serving the remainder of his sentence in Yemen, he returned to his family home in December.
If the US Court of Appeals in Washington decides to rule on the case, its decision could have ramifications for the Guantanamo military commissions called upon to issue rulings for other detainees on the same charge.
The charge of "material support for terrorism" is among the most common war crime charges the US military has made against terror suspects held at the US naval base in southern Cuba.
But critics argue the charge is not a war crime under international law, and so any such crime cannot be charged under the military commissions system. The US government says "material support" is a war crime, under the domestic common law of war.
"Material support to terrorism is not a war crime. It falls outside of a military commission's jurisdiction," Hamdan's attorney Joseph McMillan insisted to the judges. "Guantanamo is not an occupied territory, we need a law of war."
Hamdan "has not received the same kind of process that he would have received in any US court," McMillan added.
Arguing for the US government, Justice Department lawyer Joseph DePue countered that Hamdan's crime was "clearly an offense subject to be tried in front of a military commission," citing the US common law of war.
The court is not expected to rule for several months.
Hamdan, who is about 42, was detained by US forces in Afghanistan in late 2001 and arrived at Guantanamo in 2002. He was bin Laden's former driver and sometime bodyguard, but denied involvement in terrorist activities.
Between 1996 and November of 2001, Hamdan drove or accompanied bin Laden to various Al-Qaeda-sponsored training camps, news conferences or lectures, according to an indictment.