Hundreds of potential jurors will be interviewed in the search for an 18-strong panel to decide whether the group is guilty of conspiring to wage a "war of urban terrorism" in America, which also involved plotting to bomb New York's FBI headquarters and two busy road tunnels. The trial may last as long as a year.
The US government alleges that the group, which has pleaded not guilty, was led by Sheikh Omar Abdel Rahman, an Islamic cleric whose vociferous defence of fundamentalism and fiery anti-Western speeches have long worried the authorities. They claim he endorsed the use of terrorism; his speeches, and the ac ts of his followers, amounted to a seditious conspiracy to "overthrow or put down or destroy by force the government of the United States".
Prosecutors believe the sheikh had links with four Muslims imprisoned for life for the bombing attack on the World Trade Centre in February 1993, in which six people died and more than 1,000 were injured. They also claim the 12 Muslims tried to assassinate the Egyptian President, Hosni Mubarak, during a 1993 visit to the US.
America's seditious conspiracy laws make it illegal to plan unlawful acts such as bombings, although prosecutors sometimes need hard evidence that the plans were going to be acted upon if they are to secure convictions. Juries tend to see mere talk of a crime as protected free speech under the US Constitution. So the outcome may depend on the strength of the US government's physical evidence.
To that end, the government can point to the findings of the police, who say they caught some of the defendants mixing a "witches' brew" of chemicals for use in bombings in New York during the 4 July holiday weekend, 19 months ago.
They also reportedly have audio and video tapes from an informer named Emad Salem.
The sheikh, who has been in custody for more than a year, has a lengthy career as a criminal defendant, having been accused of fomenting unrest on several occasions. Before tangling with the American authorities, he was acquitted three times in Egypt - trials he used to publicise his cause. His only conviction, in Egypt in 1989, was after a trial in absentia.
The sheikh had planned to defend himself, although he speaks little English and, according to supporters, suffers from heart trouble, diabetes and - more recently - a bout of tuberculosis.
However, he has since hired two attorneys, including Lynne Stewart, one of the city's best-known lawyers.