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The Strasbourg-based court is holding a Chamber hearing in the case of Abu Zubaydah, a Palestinian born in Saudi Arabia, against Lithuania.
The 45-year-old man claims that he was held in a secret detention facility in Lithuania in 2005 and 2006 and that his treatment "amounted to torture".
Abu Zubaydah, who was captured in Pakistan in 2002, is currently held in a military prison at the US Guantanamo Bay Naval Base in Cuba.
Abu Zubaydah is the second person whose lawyers said that their client was detained in Lithuania.
Prosecutors are currently conducting a pre-trial investigation into allegations that Mustafa al-Hawsawi, a Saudi citizen, was secretly detained in the country.
Both men are charged with involvement in the September 11, 2001 attacks on the United States that left almost 3,000 people dead.
Lithuania's law-enforcement agencies said that they have not received any evidence proving that any particular individual was detained in the country and dismiss the defense lawyers' claims.