One was Mohammed Atta, who is believed to have flown one of the jets into the World Trade Center.
The German national security agency estimates there are 31,000 members of Muslim fundamentalist organisations, more than 3000 of whom are considered "potential extremists".
Germany could be harbouring as many as 30 "sleeper" agents like those who carried out the hijackings, the news weekly Stern says.
"We've discovered to our shock that there are people living among us who hate us and plan bad things against us," said Andreas Rieck, of the German Orient Institute, a think tank.
Events have pushed the authorities into taking emergency action which, by the liberal standards of post-Second World War Germany, are viewed in some corners as worryingly authoritarian.
The Government has already approved measures allowing the banning of religious groups that abuse their status by engaging in criminal activities.
The steps have gone hand-in-hand with pledges that they are aimed not against Islam but against practitioners of violence - words that are directed to home-grown far-right thugs, guilty of a string of xenophobic attacks, as much as to foreign Muslims.
The authorities have also earmarked an additional three billion marks ($3.25 billion) next year to fight terrorism. It will be spent on beefing up protection of airports and German embassies abroad and on domestic intelligence.
They have started to think about a revamp of the armed forces, which are configured for armoured battle and are unfit for nimble, commando duties abroad. And they are mulling a revision of Germany's strict privacy laws and implementing measures to prevent money-laundering.
Interior Minister Otto Schily said it was vital to give the authorities the power to probe suspected crimes. "It's fine to protect data, but this must not hamper the prevention of crime or the prevention of terrorism," he said.
As for military action, the Government should have fewer problems - in theory.
Until the 1999 Kosovo War, the German constitution and its post-Nazi era traditions precluded the country from taking part in foreign military operations. That taboo may now have been broken, but the Government is still having a hard time rallying support for sending German troops and planes to the allied cause.
One of the problems is that, unlike in Kosovo, there is the lack of clear objectives.
"Afghanistan could become a second Vietnam," said Nobel Prize-winning author Gunter Grass, contending that it was more important to tackle "the causes of hatred" than carrying out an armed assault.
Another is the deep roots of pacifism that reach right into the heart of German politics and have left the Greens, the junior partner to Chancellor Gerhard Schroeder's Social Democrats in the governing coalition, bitterly divided.
Macedonia is already a war too far for many Greens, whose support has fallen by a third since entering the Government.
Green organisations up and down the country have already started bombarding their national leadership with pacifist motions.
A significant number of Greens MPs may vote against German participation in any strikes, a move that would probably force the party to quit the coalition, taking with them the Foreign Minister, the capable Joschka Fischer.
Schroeder would then have to forge a "grand alliance" with the conservative Opposition, the Christian Democrats.
The latest public opinion poll says 69 per cent of German voters interviewed say Germany should provide only logistical help, and not combat troops, in any Afghan strikes.
Faced with such grinding pressures, the best Schroeder is likely to offer Washington is that Germany take over the role of Nato peace troops in Macedonia, thus freeing its allies to carry out the unpleasant business in central Asia.
Macedonia was to have been a short excursion for up to 500 German troops. Now up to 700 Germans are expected to provide the backbone of the new mission, looking after civilian observers.
France and Italy are expected to provide another 300 troops between them. This will be the first time since the Second World War that Germans will be in charge of an international military force.
"Germany is ready to take risks, even military ones, but isn't prepared for adventures," Schroeder said.
- HERALD CORRESPONDENT, INDEPENDENT
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America