But in one case, Haroon Aswat, judges said they could not yet give the go-ahead to extradition because they needed to see more submissions on his schizophrenia and how that would be treated were he sent to the US.
Abu Hamza is charged with offences relating to hostage taking in Yemen and an alleged plot to set-up a terrorism training camp in the United States. Haroon Aswat is also accused in connection to the training camp.
The final two men allegedly played a part in organising the 1998 US Embassy bombings in East Africa. Babar Ahmad and Talha Ahsan are accused of supporting terrorism through a website operated in London