Lawyers are appealing in a US federal court on behalf of detainees from the Afghan war held at Guantanamo Bay in Cuba, arguing that the prisoners should be charged in court or released.
The US authorities have said they intend to set up military tribunals at some stage, but so far none have been established.
Lawyers for two British Muslims, two Australians and 12 Kuwaitis are presenting their case at the US Court of Appeals in Washington DC.
The Bush administration argues that the detainees - captured in Afghanistan and Pakistan following the 11 September attacks on New York and Washington - are "unlawful
combatants".
Crackdown on al-Qaeda
The administration suspects the Guantanamo detainees of having links with Osama Bin Laden's al-Qaeda network, blamed for the 11 September attacks.
But the lawyers say the men should be taken to court, charged with an offence and given a fair trial - or released.
The appeals court case concerns:
British Muslims Asif Iqbal and Shafiq Rasul, both in their 20s, who flew to Pakistan and then to Afghanistan just before the 11 September attacks
Australian David Hicks, 26, captured by the US-backed Northern Alliance in Afghanistan - his family deny that he trained with al-Qaeda
Australian Mamdouh Habib, 47, captured by US forces in Pakistan on suspicion of al-Qaeda links
12 Kuwaitis who were in Afghanistan doing charity work, according to their families.
The Kuwaiti and Australian governments also want the US authorities to speed up the process of deciding which detainees can be released.
The BBC's Justin Webb in Washington says the US State Department is understood to be keen to get the process going as soon as possible.
But he adds that the Department of Defense is in less of a hurry, worried that some men might be released because of lack of evidence and then go on to attack American interests again in the future.
No court hearings
Three Afghans and a Pakistani were set free from Guantanamo Bay last month.
But more than 600 are still in captivity, and most have been held for more than 10 months without charge.
They are from more than 40 countries, and include about 60 Pakistanis and about 100 Saudis.
A US district judge, Colleen Kollar-Kotelly, ruled four months ago that the Guantanamo detainees had no right to court hearings - so the military can hold them indefinitely without filing charges.
The judge argued that the prisoners did not come under federal court jurisdiction as they were held outside the United States.