Lawyers for radical cleric Abu Hamza, who is wanted by the United States on terrorism charges, have said his health is "deteriorating".
They said medical tests could establish that he is unfit to plead and should not be extradited to America to face trial.
Hamza is one of a number of terror suspects who on Tuesday launched a last-ditch legal challenge at London's High court to halt extradition after the European Court of Human Rights refused to intervene over their removal.
A QC for the Home Secretary is arguing that the challenges, which mostly come at the end of marathon legal battles, are abuses of process as all the points now raised could have been raised months or even years earlier and have no merit.
Sir John Thomas, President of the Queen's Bench Division, and Mr Justice Ouseley are hearing the latest legal points over the next few days.
On Tuesday, the first day of the hearing, Sir John expressed concern that the extradition battle - also involving high-profile terror suspects Babar Ahmad, Syed Ahsan, Khaled Al-Fawwaz and Adel Abdul Bary - was threatening to "go on and on and on".
He was told that Ahmad and Ahsan are mounting a fresh challenge to Monday's refusal by the Director of Public Prosecutions (DPP) to sanction a private prosecution against them in the UK, which would mean them avoiding extradition.
Sir John said the new DPP challenge should be considered on Wednesday afternoon, adding: "If these points are good points, let's get it all out now. Otherwise these cases will go on and on and on."
Hamza's QC, Alun Jones, is arguing that there is "uncontradicted medical opinion" that an MRI (magnetic resonance imaging) scan is "medically necessary" for the cleric and a temporary injunction should be granted to allow it to be carried out. He says if tests establish that Hamza is unfit to plead, it will be contended that it would be "oppressive" to extradite him under the 2003 Extradition Act.
The QC says a judge referred to Hamza's "very poor health" at an extradition hearing in 2008. Since then his condition may have deteriorated further - "perhaps attributable to sleep deprivation and the continued confinement of the appellant in an unrelentingly harsh environment". The hearing continues.