Radical Muslim preacher Abu Hamza al-Masri has appeared at Belmarsh Magistrates' Court in London.
Mr Abu Hamza appeared in court on Thursday afternoon
The cleric faces 11 terrorism charges including hostage-taking and trying to set up a terrorist training camp in the US.
The 47-year-old was arrested at his home in west London at 0300 BST on Thursday.
The US want to extradite him over allegations of hostage-taking in Yemen and supporting terrorism.
Abu Hamza, who preaches outside a north London mosque, is appealing against removal of his UK citizenship.
Details of the charges were revealed in New York as he was appearing in court
at the top security prison in south east London.
On Thursday, his home was being searched under the Extradition Act 2003, the street is cordoned off and items were seized, including videos, documents and a briefcase.
The cleric has never been convicted of any terrorism offences in the UK, but Yemeni authorities accuse him of being involved in attacks there in 1998.
BBC social affairs correspondent Daniel Sandford said the FBI is thought to have built a case against him using information from James Ujaama, who is in prison in America.
The hearing before Bow Street magistrates sitting at Belmarsh is likely to be the start of a lengthy court battle.
It is likely to be several months before a formal committal hearing at which a district judge will look at the evidence and decide whether it is strong enough for extradition.
The Egyptian-born preacher is already at the centre of a deportation battle with the Home Office, which wants to remove his citizenship, gained through marriage in 1981.
The government claims that he has provided support and advice to terrorist groups, including al-Qaeda.
He had been a regular preacher at the Finsbury Park mosque until he was banned by the Charity Commission in February 2003.
Journalists were waiting for the police van as it arrived at Belmarsh
It accused him of abusing his position for "personal and political, rather than charitable purposes".
But he has continued to preach to worshippers outside the mosque, which was closed for repairs after a police raid in January 2003.
Mr Abu Hamza's lawyer, Muddassar Arani, said she had been surprised by the arrest and knew nothing of the charges.
She spoke to her client by telephone and said: "He is quite calm about it. He said: 'Take your time and come down whenever you can'."
She told BBC Radio 4's Today programme that extradition would have to be based on something that had happened in the US.
"I really can't comment on what is being alleged to have happened in America," she said.