The trial has begun in Florida of US citizen Jose Padilla and two other men for conspiracy to murder US nationals and aiding Islamic extremists.
Jose Padilla was arrested at Chicago airport in May 2002
After his arrest in 2002, Mr Padilla was accused of planning to detonate a radioactive bomb and held in a military jail without charge for three years.
That allegation will not be part of the trial in Miami.
Prosecutors opened their case saying the three were part of a secret terror support cell based in south Florida.
Defence lawyers said that the charges against the three were "a lot of rhetoric" but showed "no evidence".
The BBC's Andy Gallacher in Florida says some critics are calling the case "Padilla Lite" because the most serious accusations have been dropped.
However, prosecutors say that an application form to attend an al-Qaeda training camp in Afghanistan will prove that Mr Padilla, also known as Abdullah Mujahir, was connected to Islamic extremists.
Adham Amin Hassoun and Kifah Wael Jayyousi, both 45, are also being tried alongside Mr Padilla. All three could face life sentences if found guilty.
Assistant US attorney Brian Frazier, prosecuting, told jurors: "Jose Padilla was an al-Qaeda terrorist trainee providing the ultimate form of material support - himself.
"Padilla was serious, he was focused, he was secretive. Padilla had cut himself off from most things in his life that did not concern his radical view of the Islamic religion."
Lawyer Jeanne Baker, representing Mr Hassoun, said: "The government really is trying to put al-Qaeda on trial in this case and it doesn't belong in this courtroom.
"The government is twisting the facts out of all recognition."
Mr Padilla, a former Chicago gang member of Puerto Rican descent, is a convert to Islam.
He was arrested at Chicago's O'Hare Airport in May 2002 after returning from Pakistan.
Mr Padilla was held at a US naval base in South Carolina for more than three years. He says he was tortured. US officials deny that he was abused.
Following a long battle between the Bush administration and civil liberties groups, Mr Padilla was transferred to the civilian courts in 2005.
The case is expected to last for months and is being seen as an important test of the Bush administration's war on terror, our correspondent says.
Jeffrey Harris, president of the Florida Association of Criminal Defence Lawyers, said: "This is a showcase trial that will be publicised all over the world. It doesn't get much bigger than this."