Lamine and Ibrahim Adam breached orders and are missing
The government's controversial anti-terror control orders are set to be challenged in the House of Lords.
Ten terror suspects placed under the measures - at least two of whom are on the run - will argue they violate their rights to liberty and a fair trial.
Five Law Lords will also consider Home Secretary Jacqui Smith's appeal against a ruling which said orders imposed on six Iraqis breached their human rights.
Control orders place terror suspects under curfews of up to 18 hours a day.
Opponents say they amount to "virtual house arrest" and are often based on evidence which is not made public.
Eric Metcalfe, of human rights and law reform organisation Justice, said: "We cannot allow the fight against terrorism to compromise basic fairness.
"No-one should be subject to virtual house arrest without knowing the evidence against him and being able to challenge it in a fair and open manner."
Counter-terrorism experts have urged the government to prosecute more terrorism suspects rather than over-use control orders.
Among them is the government's own independent terror watchdog Lord Carlile.
Earlier this week, Home Office minister Tony McNulty said the control order system might be "inappropriate".
"It may be that we haven't thought in rigorous enough terms on how we capture these individuals under the law," Mr McNulty said.
The six Iraqis won a victory in the Court of Appeal last year when it was ruled that control orders placed on them were incompatible with Article 5 of the European Convention on Human Rights.
One of the men, Bestun Salim, subsequently vanished and is still at large.
'Mockery of security'
James Welch, from human rights group Liberty, said: "Punishing people and their families without trial makes a mockery of British justice.
"Labelling people as terrorists and leaving them in the community makes a mockery of security.
"Only charges, evidence and proof will protect our lives and our way of life in the long-term."
Control orders were introduced in 2005 after Law Lords ruled it was unlawful to incarcerate, without trial, terror suspects who could not be prosecuted or deported because of concerns over their human rights.
The Home Office has said seven out of 17 individuals currently on control orders have absconded, although one has since handed himself in.
The judges, headed by Lord Bingham of Cornhill, are expected to deliberate for six days.