Binyam Mohamed is among the men behind the damages claim
Six former Guantanamo Bay detainees are to hear if an appeal has succeeded against government use of secret evidence to fight their damages claim.
The UK citizens and residents are suing intelligence agencies and ministers for alleged complicity in their abuse.
Their barristers have argued that the "closed material procedure" was never intended for use in civil actions.
The government defended itself saying some of the evidence was so sensitive it had to be presented in secret.
Binyam Mohamed, Bisher Al Rawi, Jamil El Banna, Richard Belmar, Omar Deghayes and Martin Mubanga have all denied any involvement in terrorism.
They allege that MI5 and MI6 aided and abetted their unlawful imprisonment and extraordinary rendition to various locations around the world, including Guantanamo, where they say they suffered torture and inhuman and degrading treatment.
The intelligence services, Attorney General Baroness Scotland, the Foreign Office and the Home Office are contesting the claims.
The Master of the Rolls, Lord Neuberger, Lord Justice Maurice Kay and Lord Justice Sullivan will decide today the issue of whether large parts of the security services' and government's defence can be kept secret from the former detainees, their lawyers and the public.
The six men lodged their appeal after Mr Justice Silber ruled in the High Court in November last year that there was no reason in law why the court could not allow a "closed material procedure" to be used in a claim for damages.
This would mean that the government and security services would not have to disclose information to the claimants' lawyers if they felt that doing so would damage the interests of national security, the UK's international relations, the detection and prevention of crime, or was likely to harm the public interest in some other way.
Instead, the material would be disclosed to "special advocates" - barristers given security vetting and clearance. These lawyers would be able to take instructions from the claimants, but only in advance of seeing the material the government did not wish to disclose.
Dinah Rose QC, who represents five of the six men, said use of the procedure would mean that they would never know the case they were being asked to answer.
"This is incompatible with the basic concepts of the civil trial," she said.
A number of media organisations, including the BBC, and the human rights groups Justice and Liberty are also intervening in the case.
They are arguing that the government's secrecy proposals breach the right to a fair and open trial, and are contrary to the right to freedom of expression and the public's right to know what the authorities are or have been doing on its behalf.
It is thought likely that whichever side the judges come down on the case will continue in the Supreme Court.