The twin towers were destroyed by controlled explosion

Truthers say video footage of the buildings falling points to demolition due to the way the towers bend before collapsing. Also, there appear to be explosions as the windows blow out, floor by floor, from the top downwards. One US academic claims to have tested samples from the wrecked towers which show the presence of chemical residue, suggesting explosives had been used.

But in controlled explosion demolition experts collapse a building from the bottom not the top. Experts say the windows were blown out as each floor collapsed on to the one below, sending debris and office equipment flying out.

It would also have taken considerable work, which would not have gone unnoticed, to plant sufficient explosives the length of the buildings to bring them down.

The Pentagon was hit by a missile, not a plane

The evidence for this, say sceptics, is that the major damage to the building comprised a roundish blast hole, not the more extended destruction some say would be caused by aeroplane wings. Truthers claim parts of a scrapped plane, including the tail, were moved to the Pentagon as part of the fabrication.

This theory ignores the considerable evidence of the bodies of passengers and crew at the site which were photographed. Thousands of people saw the plane circle then fly into the Pentagon. Some quickly photographed the scene. Anyone planting plane debris at the site afterwards would surely have been seen.

World Trade Centre building 7, adjacent to the twin towers, must have been was destroyed by controlled demolition because it was not hit by a plane

This theory is partly based on a remark by the owner of the building who, fearing it was about to collapse, said firefighters inside should be brought out immediately. He used the words: "Pull it". This remark has been interpreted as slang for demolishing the building. In fact, the collapse was caused by intense fires in one of the neighbouring twin towers that spread to WTC 7, causing its steel beams to buckle and the building to come down.

The hijacked planes were packed with explosives and flown by remote control

Some conspiracy theorists believe the passengers supposedly on board were either killed elsewhere and their bodies dumped at sea, or were part of the conspiracy and are now in hiding with new identities. A key piece of evidence claimed for this theory is that the mobile phone calls the victims are recorded as having made to loved ones from the doomed planes were not possible because of the altitude of the aircraft and therefore faked using "voice morphing technology".

However, phone records show the calls were made from satellite phones fitted to the back of the aircraft seats.

Israel was behind the attacks in order to draw America into a conflict with Arab nations

The evidence claimed for this theory is that 4,000 Jews who supposedly worked at the WTC failed to report for work on 11 September because they had been forewarned by the Israeli intelligence service, Mossad.

However, the figure appears to be based on a statement made by the Israeli foreign minister that about 4,000 Israelis were in the cities under attack at the time. More than one in ten of those who died on 9/11 were Jewish.

The fourth plane, apparently headed for the White House, was shot down by a missile

An order had gone out from President Bush for the flight to be shot down if necessary, but before this could be carried out passengers attempted to charge the hijackers, who flew the plane into the ground in Pennsylvania.

There was insider trading in the stocks of the two airlines whose planes were hijacked, United and American, suggesting powerful people knew the attacks were coming

The trading has been tracked to other causes.