Moussaoui, a 37-year-old Frenchman of Moroccan descent, was arrested in August 2001, weeks before the world's deadliest terror attack, which killed nearly 3,000 people.
Prosecutors contend he knew in advance of the strike and did not mention it to FBI investigators and is just as guilty as the 19 hijackers who steered fuel laden airliners at landmarks in New York and Washington.
In a statement in April 2005, Moussaoui admitted to six counts of conspiring with Al-Qaeda to fly airliners into US government buildings.
But he has maintained he was due to fly a jetliner into the White House as part of a follow-up wave of attacks and not the September 11 strikes.
A jury is first being asked to decide whether Moussaoui is eligible for the death penalty, and if he is, whether he will receive it.
The alternative punishment is life in prison, without possibility of parole.
Jury selection
Judge Leonie Brinkema presided over a process to whittle down the remaining pool of 83 potential jurors, to the final panel of 12 people and six alternates who will hear the case.
Moussaoui was led into court wearing a green prison jumpsuit, with a white knitted skullcap and lounged in his chair, guarded by two security agents.
There was no repeat of his outbursts on the first day of jury selection, when he berated the judge, his court appointed lawyers and declared "I am Al-Qaeda," earning himself repeated expulsions.
Instead, he sat, and continually surveyed lines of jurors waiting their turn to be accepted or rejected on the public benches, stroking his thick, black beard and occasionally writing a note on a legal pad.
Prosecution lawyers were due to open the case after a lunchtime recess with a 45-minute opening statement laying out the case for Moussaoui's execution.
Moussaoui, a self-proclaimed "slave of Allah," had a rough childhood in southwestern France before hearing the call to jihad for the first time at mosques in London, where he studied international business.
Tight security
Police clamped tight security around the courthouse in Alexandria, Virginia, just outside Washington, the venue for the death penalty phase of Moussaoui's hearing.
Roads were closed around the building, a few kilometers from the Pentagon, charred in the 2001 attacks. Police marksmen and spotters watched from the roof of a nearby apartment building.
Relatives of September 11 victims have been invited to watch the trial, expected to last between one and three months, on closed-circuit television in five courthouses around the country.
Malaysia link
According to the independent US commission which investigated the September 11 attacks, Moussaoui travelled to Malaysia and met Khaled Sheikh Mohammed, who is credited with being the brains behind the 2001 attacks.
He then travelled to the US and took flying lessons in the state of Oklahoma before moving again to Minnesota where he trained on a 747 Flight simulator.
Prosecutors would never have been able to prove that he would have taken part in the September 11 attacks had he not been arrested for overstaying his visa and arousing suspicion.
The prosecution has signalled it plans to call relatives of victims of the September 11 attacks in the second phase of the trial if Moussaoui is judged liable to face the death penalty.
But defence lawyers may also embarrass the government, possibly by arguing that the FBI knew far more about the September 11 strikes than it has previously admitted.