Using Web-based television as well as Internet chat rooms, “news” sites and what amount to virtual training camps for terrorism and guerrilla warfare, they keep up a constant rant of propaganda, indoctrination and ideological discussion about how best to defeat the United States. Famous examples include Osama bin Laden’s address to the American people on the eve of the 2004 presidential election, using rhetoric and examples that seemed to have been drawn from Michael Moore’s film “Fahrenheit 9/11.” One of Al Qaeda’s increasingly prominent spokesmen is an American convert to Islam, Adam Gadahn, known as Azzam al-Amriki. In May, bin Laden’s colleague Ayman Al-Zawahiri issued a slickly produced Web video with English subtitles in which he commented on recent headlines: the faltering U.S. troop surge in Iraq, health-care problems for American veterans, even global warming.

Other Qaeda ideologues are less well known but equally influential. One is the red-haired Syrian known as Abu Musab al-Suri. Before his capture in Pakistan in 2005 (his current whereabouts are unknown), al-Suri wrote thousands of pages that outlined not only his thinking about “global jihad” but the methods he deemed necessary to carry it out. They continue to circulate widely on the Web. Al-Suri had once run a Qaeda camp in Afghanistan, and proposed ways to teach some of the same lessons in the hostile environment of the West. He published lists of potential targets, including the London Underground. The key, said al-Suri, is “individual terrorism” that cannot be thwarted by the disruptions of a command structure. Those killed on 9/11 and afterward are just a beginning, he said. “Our mujahideen [holy warriors] have only collected a small amount of the bill.”

Traditionally this kind of propaganda had more appeal to people from Muslim lands that lived under colonialism in the 20th century, who are convinced that the injustices of foreign occupation are continuing in the Palestinian territories, Afghanistan and Iraq. While the Internet dissertations are full of religious references, it’s U.S. government policies that give them their persuasive power. “They are popular not because of their ideology but in spite of it,” says Abdelwahab El-Affendi, an expert on radical Islam at Britain’s University of Westminster. “The way they portray themselves is usually repugnant to most people, but they make up for it by saying ‘We are the only ones who are fighting the real battle to defend the ummah [the community of Muslims]’.”

Some American analysts worry that the United States isn’t fighting back hard enough in this cyberwar of ideas. “We have failed to take the jihadists seriously, intellectually and culturally, and as a result their corrosive influence is progressing unopposed,” warns Stephen Ulph, a research associate of the Combating Terrorism Center at West Point. But others believe the best defense lies in a core concept as old as the nation. For most Muslims, says Gistaro, “the American dream is real.” As long as that’s the case, Al Qaeda’s Internet imams will find it hard, or impossible, to find new recruits here.