Lawyers for Abu Hamza are asking the High Court for time to carry out further medical tests as he renews his long-running legal battle to halt his extradition from the UK to the US.
His lawyers say Hamza's health is "deteriorating".
Abu Hamza was in custody in New York today awaiting trial on charges of bombing two United States embassies in Africa.
Radical cleric Abu Hamza has appeared in front of a New York court following his extradition from the UK. He did not enter a plea.
Abu Hamza and four other terror suspects have left prison and are on route to the US where they face terror charges.