European judges will rule later whether six terror suspects, including radical Muslim cleric Abu Hamza al-Masri, can be extradited from the UK to the US.
They include alleged terror fundraiser Babar Ahmad and two men accused of a role in two 1998 US embassy bombings.
The European Court of Human Rights has considered whether human rights would be breached if the men receive lengthy sentences in certain prison conditions.
The suspects say they could be held in solitary confinement.
They argue that they might be held in a high-security prison in Colorado, known as a "supermax" prison and claim that if convicted there is very little or no prospect of ever being released.
The six suspects, who have been indicted on various charges of alleged terrorism in the US, say conditions of detention at a so-called "supermax" prison would amount to ill-treatment under article three of the human rights code.
The European code states: "No-one shall be subjected to torture or to inhuman or degrading treatment or punishment".
European judges halted extradition proceedings concerning the suspects in July 2010, arguing that the court needed more time to consider complaints that transferring the men risked breaching their rights by exposing them to possible life imprisonment without parole and solitary confinement.
Earlier this year, the European Court ruled that Jordanian terror suspect Abu Qatada could not be sent for trial from the UK to his homeland because evidence obtained by torture might be used against him.
BBC home affairs correspondent Danny Shaw says the ruling involving the six suspects is "potentially more significant as it concerns the government's ability to extradite suspects to one of Britain's closest allies, the US".
Egyptian-born Abu Hamza, who was granted British citizenship in 1986, rose to prominence when he was a preacher at Finsbury Park mosque, in north London.
He is serving a seven-year sentence in the UK for inciting racial hatred.
He is wanted in the US on 11 charges related to claims that he took 16 hostages in Yemen in 1998, promoted violent jihad in Afghanistan in 2001 and conspired to set up a jihad training camp in the state of Oregon.
US authorities have described him as a "terrorist facilitator with a global reach".
Babar Ahmad, 37, has been held without trial in a UK prison for nearly eight years.
And he has been refused bail since his August 2004 arrest on a US extradition warrant.
The British Muslim denies terror-related charges.
Four other men - Haroon Rashid Aswat, Seyla Talha Ahsan, Adel Abdul Bary and Khaled Al-Fawwaz - will also be subject to the ruling made by European judges.
Mr Al-Fawwaz and Mr Bary are accused of being involved in US Embassy bombings in Kenya and Tanzania in 1998.
Mr Aswat is accused of a being part of an alleged terror camp in Oregon and Mr Ahsan is accused by a US court of running an extremist website and funding the Taliban.