A last-ditch legal move by radical cleric Abu Hamza to fight extradition to the United States will be heard by the High Court next week.
Two judges in London will also consider a challenge by a second terror suspect, Khaled Al-Fawwaz, next Tuesday.
The men are seeking injunctions preventing their removal from the UK.
Pending the hearing of their applications by Sir John Thomas, President of the Queen's Bench Division, and Mr Justice Ouseley, interim injunctions have been issued preventing their removal.
The latest legal action comes after Europe's human rights judges this week rejected a bid for an appeal by Hamza and four other terror suspects, paving the way for their extradition.
A panel of five judges threw out their request to the Grand Chamber of the European Court of Human Rights.
Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred, has been fighting extradition since 2004.
Computer expert Babar Ahmad, who was also subject to this week's ruling, has been held in a UK prison without trial for eight years after being accused of raising funds for terrorism.
After the ruling in Europe, the Home Office said Hamza and Ahmad, with Seyla Talha Ahsan, Adel Abdul Bary and Al-Fawwaz, would be "handed over to the US authorities as quickly as possible".
A Home Office spokeswoman said: "The European Court of Human Rights ruled there was no bar to the extradition of these men. We will continue working to ensure they are handed over to the US authorities as soon as possible."
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