Abu Hamza will face extradition to the US on a series of terrorism charges after he has served his UK prison term for inciting murder and race hate.
The extradition request against Hamza dates from 2004
A US indictment filed in 2004 accuses the cleric of terrorism in the Yemen.
The charges also allege he tried to set up a training camp in Oregon, and provided money to recruits for al-Qaeda instruction in Afghanistan.
The extradition proceedings - adjourned pending Abu Hamza's Old Bailey trial - would be contested, his lawyers said.
Defence counsel Edward Fitzgerald QC said the Yemeni allegations had been investigated by the Metropolitan Police but had not lead to any charges.
Extradition would also be fought on the grounds of conditions Abu Hamza may find himself being detained under - possibly at the Guantanamo Bay camp in Cuba or in solitary confinement elsewhere, he said.
The United States Department of Justice said the US "stands ready to resume the extradition proceedings against Abu Hamza when British law allows".
Its indictment alleges Abu Hamza provided a satellite phone and funding to the group responsible to the kidnapping of 16 Western tourists in Yemen in December 1998, in which four lost their lives.
Two of the counts also concern claims Abu Hamza tried to set up a terror training camp in Oregon between 1999 and 2000 to "fight jihad" in Afghanistan.
James Ujaama - an alleged former worshipper at Finsbury Park Mosque, who is also named in the indictment - has pleaded guilty to involvement in a plot and was sentenced to two years in jail after agreeing to help the US authorities.
When the US unveiled the allegations against Abu Hamza, New York Police Commissioner Raymond Kelly described the cleric as a "freelance consultant to terrorism groups worldwide".
Mr Kelly said: "He is suspected of providing support to trainees in Osama bin Laden's terrorist camps as well as dispatching associates from England to help establish jihad training sites here in the US."
And ultimately it was the extradition request that lead to Abu Hamza's appearance in an Old Bailey dock.
When Scotland Yard officers executed the extradition warrant issued by Bow Street magistrates they searched his Shepherd's Bush home.
It was there they seized the video and audio tapes which formed the basis of the central charges in the trial.