Eight years of high-profile legal argument are now over for the UK.
The European Court of Human Rights in Strasbourg has rejected an appeal against extradition by five terrorist suspects, including Abu Hamza al Masri.
It means they are now likely to be extradited to the US within weeks.
Abu Hamza is accused of planning a terrorist training camp in the US and assisting hostage-taking in Yemen. He has been in custody since 2004.
Two of the men have been held since 1998 – the longest time without trial in the UK.
The men had appealed against their extradition, arguing that they would face inhumane treatment in the US if sent there.
But the ECHR decided the potential sentences they face are not disproportionate to the crimes they are accused of.