The suspects are held in a high security jail in south-east London

They are among 13 suspects held at Belmarsh high security prison in London under the 2001 Anti-Terrorism and Security Act, which came into force after the 11 September attacks on the US.

Some of them have been in custody without charge for 18 months.

The appeals began on Monday and are expected to last several months.

'Al-Qaeda links'

Lawyers representing the Home Office told the hearing the men were involved with a number of Middle East or North African terrorist networks, and trained in Afghanistan.

The government also says they had links with extremist spiritual leaders in the UK, one of whom was claimed to be the radical cleric Abu Hamza.

Wyn Williams QC argued that Abu Hamza, along with another spiritual leader who can only be identified as K, preached an anti-Western message which encouraged young Muslims to join extreme causes overseas.

Monday's proceedings focused on three alleged international suspects who it claimed supported banned organisations and were linked to al-Qaeda.

Abu Hamza faces being stripped of his British citizenship

It was alleged they provided assistance, including satellite phones, to extremists abroad and they associated with convicted terrorists.

Lawyers at Monday's appeal hearing also discussed how much information could be reported as there was a danger that the names of the suspects could leak out, particularly to the suspects' countries of origin.

The BBC's home affairs correspondent, Margaret Gilmore, said: "This is a landmark case and a real test of the stringent anti-terrorist powers introduced after September 11."

The decision by Home Secretary David Blunkett to invoke the powers of the act to detain the suspects indefinitely was controversial.

The act says people can be held if they pose a threat to national security or have links to international terrorism but are foreign nationals who cannot be deported.

A three-man panel, headed by Mr Justice Ouseley, is to hear the appeals of the 10 men.

Two others who were being held with them have now left the country. They are also taking action against their detention.

Deportation

Only two of the suspects have been named - Abu Rideh and Djamel Ajouaou.

The Court of Appeal has ruled that the government was correct in law to detain the men.

And an independent review concluded in February that the criteria for detaining them was met in every case.

Mr Blunkett intends to use new immigration powers to deport Mr Hamza on the grounds he has encouraged people to fight against Britain.

But the Egyptian-born cleric has denied any involvement in terrorism and has lodged an appeal.