The most fanciful park in Paris, and one of the least known, set among the city's poorest immigrant neighborhoods, is the Buttes Chaumont. A craggy mountain rises out of a taciturn lake, and a narrow path leads across what's called the "Bridge of Suicides." Muslim boys trained there last year for holy war in Iraq. Several were in their teens, born and raised in France, and many knew nothing more about guns and bombs than what they'd seen in movies. Some spoke no Arabic. But they heard the call to jihad that was raised by radical Islamist preachers, and they answered it. One died in Fallujah. Three are known to be imprisoned in Iraq, at least one of them in Abu Ghraib. Three others are jailed in France. One blew himself up in an attack on the road to Baghdad airport.

The boys had little impact on the Iraq war. But they represent a growing threat to Europe--and, some studies suggest, to the United States. Over the last three years, starting even before the overthrow of Saddam Hussein, the Jordanian terrorist Abu Mussab al-Zarqawi and groups close to him developed a sort of underground railroad to smuggle zealous fighters from Europe through Turkey and Syria into Iraq--and home again, if they survived. Now those recruits have been joined by a stream of young Islamists from Western Europe who are making their own way to the battlefield. Some are looking for Paradise as "martyrs," some just for street cred back home and some for serious combat experience in urban warfare. "Those who don't die and come back will be the future chiefs of Al Qaeda or Zarqawi [groups] in Europe," says French terrorism authority Roland Jacquard.

"We're watching very closely," says Gijs de Vries, the European Union's counterterrorism coordinator. "It only takes one or two dedicated individuals to create serious damage." All over Europe, in fact, investigators now face the threat of terrorists who are virtually self-taught, organized in groups with little or no central command and united by their obsession with the jihad against Americans in Iraq. "It has become a battle cry for Islamists around the world," says Michael Taarnby, author of a report on terrorist recruiting for the Danish Justice Ministry. Their most devastating blow to date was not inside Iraq but in Madrid last year, when a gruesome bombing spree killed 191 people in retaliation for Spain's presence in Iraq.

At a conference marking the anniversary of the Madrid atrocity last week, Robert Leiken of Washington's Nixon Center presented a provocative study of 373 radical Muslim terrorists arrested or killed in Europe and the United States from 1993 through 2004. His conclusion: some 87 percent are from immigrant backgrounds, but 41 percent are Western nationals, either naturalized, second generation or converts to Islam. "More French nationals were arrested than nationals of Pakistan and Yemen combined," says Leiken. While homegrown Muslim terrorists have so far been rare in the United States, in Europe they virtually recruit themselves, and Leiken points out that those who have European passports have almost open access to American territory through an ongoing visa-waiver program.

All this becomes especially disturbing in light of a recent notice circulated by the U.S. Department of Homeland Security suggesting Al Qaeda's leadership has asked Zarqawi, officially Osama bin Laden's ally and "prince" in Iraq since last year, to expand his grisly terror campaign into Europe and the United States. As early as 2002, Zarqawi understood the potential for recruiting "Euro-jihadists," and the attraction the impending Iraq war would have for them. In February of that year, according to recently unsealed Spanish court documents, Zarqawi set up a meeting in Istanbul with prospective North African allies.

He proceeded to build a new network of existing cells spanning Western Europe, effectively creating a second Qaeda. The overall direction came from members of his Tawhid group in Germany, according to papers presented by Italian prosecutors. Other participating cells have been traced to Spain, the Netherlands, Britain, France, Switzerland, even Norway. Apart from their shared religious extremism, they answered to no racial or national profile. There were women as well as men. Some had no papers; some had legal refugee status. Some were European citizens.

Recent arrests suggest how Europe's ji-hadi movement has grown. In Germany, for example, officials rounded up 22 people in the city of Ulm and charged them with forging passports and other travel documents that could be used for travel to Iraq. A few weeks ago, near Mainz, the Germans arrested an Iraqi identified only as Ibrahim Mohamed K., who was charged with trying to enlist a Palestinian immigrant in Germany for a suicide mission in Iraq. More ominously, Ibrahim Mohamed K. was also accused of trying to obtain 48 grams of enriched uranium through a middleman in Luxembourg so he could make a radiological "dirty bomb."

Since the Madrid bombings, police across Europe have intensified their crackdowns. But as old cells are dismantled, new ones emerge to take their place. Often they are close-knit groups of friends and relatives, making them even harder for investigators to crack. "That frustrates the security services," says Taarnby. But the news isn't all bad. "It's also a frustrating situation for the wanna-be jihadists," Taarnby says. "How do they join? You need to know someone. You don't just buy a ticket to Baghdad." The arrests and surveillance in Western Europe have in many cases focused on the "gatekeepers," often associated with radical mosques, who facilitated travel to Iraq and earlier jihads. Tape transcripts submitted to Italian courts, for instance, show that the police have not only bugged phones, cars and apartments, but the mosques themselves.

And yet the jihad keeps growing. Outside the wrought-iron fences of the Buttes Chaumont, you can get a glimpse of why. Dozens of grim housing projects loom out of barren pavements. Some of the immigrant-filled towers have police outposts designed into their ground floors. Unemployment is as high as 60 percent, according to a municipal official. Kids spend the day in second-rate schools and then loiter in the streets with nothing better to do. "They have French nationality but they don't have a job," says Sabah Khadim, a senior official at the Interior Ministry in Baghdad. "They don't have a good life. And Iraq becomes an attractive place." Until that pattern is broken, the lure for Euro-jihadists will persist--as will the risks for the rest of us.

With Tracy McNicoll in Paris, Stefan Theil in Berlin, Jacopo Barigazzi in Milan and Babak Dehghanpisheh in Baghdad