Representatives for 14 prisoners - 11 Kuwaitis, two Britons and an Australian - told a US court that the detainees were being denied their rights of seeing a lawyer or having their cases determined by an impartial body because they were being held by the US military.
The Britons and the Australian are seeking a court order to be released from Camp X-Ray, while the Kuwaitis want to be allowed access to their lawyers.
The petitions were argued against by the US Department of Justice and the judge involved has yet to decide if she has the authority to intervene.
In a separate but related case, a court rejected a request by a lawyer to represent another Guantanamo detainee.
'Base not US land'
Department of Justice lawyer Paul Clement said the 14 Camp X-Ray prisoners did have rights but could not enforce them through the US courts as Guantanamo Bay is not US territory.
But Thomas Wilner, representing the 11 Kuwaitis, said US courts had previously recognised the rights of people in areas under US control, such as the naval base in Cuba.
Joseph Margulies, the lawyer for the Britons and Australian, said of the case: "This raises the spectre of arbitrary, unlimited detention."
US District Judge Colleen Kollar-Kotelly did not say when she would rule on whether she had the authority to hear the case.
In the other challenge to the US handling of prisoners taken in the war in Afghanistan, an appeals panel in Richmond, Virginia, rejected the request of Frank Dunham to represent US-born suspect Yaser Esam Hamdi because they had no official relationship.
But a second petition filed on behalf of Mr Hamdi by his father asking for legal representation was allowed and Mr Dunham was appointed under that.
But the ruling by the Fourth Circuit Court of Appeals did not address the larger issue of whether Mr Hamdi, as an American-born man, was entitled to a lawyer or whether the US Government can continue to detain him.
At present about 560 prisoners are being held at Camp X-Ray.