The radical Muslim cleric Abu Hamza and four other terrorism suspects have lost their appeals against extradition from Britain to the United States.
On Monday, a panel of the European court's highest judges declined to refer the case of Abu Hamza and four other terrorism suspects to the European Court's Grand Chamber - the last avenue of appeal open to them in their fight against extradition to the US.
The men argued they will face inhumane treatment in the US if they are sent there.
They are likely to be extradited within weeks.
Abu Hamza faces charges in the US of planning a terrorist training camp in Oregon and assisting with hostage-taking in Yemen.
His legal battle has lasted more than eight years and cost millions of pounds.