Zarqawi’s green-eyed mother, Um Sayef al-Khalaylah–interviewed before her death earlier this month–also scoffed at the idea that her 37-year-old son was a terrorist big shot. “Al Qaeda is rich. If my son worked with Al Qaeda do you think my house would be like this?” she had asked, gesturing at her austere surroundings.

U.S. officials insist there’s no question Zarqawi is now a major terrorist leader. In fact, Bush administration officials have made a conscious decision to portray him as the Next Bad Guy in the war on terror, possibly the successor to Osama bin Laden, who is said to be on the run in Afghanistan. That’s one reason why, in recent weeks, officials were so eager to publicize a 17-page terror memo that Zarqawi allegedly sent to the Qaeda chieftain, and why they were so quick to name Zarqawi as the culprit behind the horrific bombings of Shiites in Iraq that preceded the Madrid train attacks by a week. In addition to numerous attacks in Iraq, Zarqawi was implicated in a bomb plot in Morocco last year–raising questions of whether any link exists between him and the Moroccans arrested in Spain late last week.

But here’s the problem. Unlike bin Laden, no one can say what the round-faced Zarqawi even looks like today. Like many current terrorist cell leaders, Zarqawi is a graduate of bin Laden’s Afghan training camps, and one thing he may have learned from the master’s mistakes is the virtue of staying anonymous. In fact, for a long time authorities haven’t even known how many legs he has, much less where he is. Before the Iraq war, one article of indictment against Saddam was that he had supplied Zarqawi with medical treatment in Baghdad–including a prosthetic leg–after the latter was badly wounded in Afghanistan. But that appears to have been based on more bad intel. Senior U.S. military officials in Baghdad tell NEWSWEEK they are now convinced Zarqawi has two fully functioning legs.

Authorities do know a few things about his network. According to Shadi Abdallah, a Jordanian-born refugee in Germany who became an informant, Zarqawi’s group, Al Tawhid, has several cells in Europe. In Abdallah’s debriefings with German investigators–copies of which were obtained by NEWSWEEK–he said one Zarqawi cell was headed by the spiritual leader of an obscure London mosque allegedly attended by Zacarias Moussaoui, the French-born jihadi awaiting trial in Virginia, and Richard Reid, the London-born petty criminal convicted in Boston of trying to blow up a U.S. airliner using a shoe bomb. But officials are stumped about Zarqawi’s whereabouts today–they know only that he is just one of many such threats facing America and its allies. “Dozens of such groups exist,” CIA Director George Tenet told Congress two weeks ago. “I’ve identified the Zarqawi network, the Ansar al-Islam network in Iraq, the Libyan Islamic Fighting Group and the Islamic Movement of Uzbekistan.”

The Qaeda organization that committed the horrors of 9/11 was, at the time, the only group that had declared global war on America. While it had widespread cells, it was anchored in Afghanistan as well. Al Qaeda also had a well-established history: bin Laden had emerged from the mujahedin movement against the Soviets and unit-ed with his deputy, Ayman al-Zawahiri, who had cut his teeth on the Islamist struggle against Egypt’s secular leaders. Now, says Milt Bearden, a former CIA station chief in Pakistan, “I think the [terror threat] has metastasized to the point where we haven’t got a clue where it will pop up next.”

The last two weeks of mass killings–of celebrant Shiites in Iraq and Pakistan on the holy day of Ashura, followed a week later by the attacks on commuters in Madrid–may some day be viewed as the opening shots fired by this spectral second generation of terrorists. In both cases authorities remain fairly clueless as to which groups were involved and to whom they are linked, whether they take orders from Al Qaeda or merely coexist with it, and whether non-Islamist groups like the Basque ETA have grown new synapses connecting them with otherwise disparate movements. All that is known is that such groups seem to be fueled by ever more virulent anti-American sentiment, and that since the war in Iraq this has often manifested itself through attacks on U.S. allies such as Spain, and agencies like the Red Cross or United Nations that work with Washington. In a videotape last fall, bin Laden specifically named Spain as a potential target. Intelligence officials also tell NEWSWEEK that Zarqawi is viewed as a suspect in three major attacks in Iraq last year: on the U.N. headquarters in Baghdad, on a leading Shiite mosque in Najaf (in which a pro-U.S. ayatollah was killed) and on an Italian paramilitary post.

For Americans, the reality of this new shadow war hasn’t hit home yet–even though the millions who ride commuter trains are queasily aware of how easily a Madrid could happen here. Since 9/11, the clenched fist of American power has struck two mighty blows–one in ousting the Taliban in Afghanistan, the other in taking out Saddam. In doing so, President George W. Bush has reasserted American power in a region where U.S. officials believe that an image of weakness invites attack.

The question now, though, is whether that giant American fist has effectively smashed down on a blob of mercury, sending it in myriad directions and making it all but untraceable. NEWSWEEK has learned that the last Orange terror alert in December–triggered by hijacking threats to foreign airliners heading to America–was based on what appears to be bad information. No arrests or detentions have been made, and no leads remain open. U.S. officials say that, even in the wake of Madrid, the level of intelligence “chatter” about an attack on the continental United States remains low; but if it was “high” in December, does today’s lack of intel mean anything? A former senior counterterrorism official in the Bush administration points out that “there have been more major terror attacks in the 30 months since 9/11 than in the 30 months before. I think we may have cut off Al Qaeda’s head, but the rest of the body is working fine and has spawned 10 more smaller heads.”

Administration officials argue that the smaller, depleted groups out there today probably couldn’t produce an attack as sophisticated as September 11’s. And they point out that there has been no major attempt to attack the U.S. homeland since then. But Madrid was devastating, occurring just across the Atlantic, especially considering that a major goal of Al Qaeda and other groups has been to weaken and disrupt Western economies. “For most major cities, transit systems are very critical to the functioning of the local and regional economy,” says Stephen Flynn, a former Coast Guard commander and author of the forthcoming book “America the Vulnerable: How the U.S. Has Failed to Secure the Homeland.” Flynn plays down the fact that the homeland’s been terror-free. “We thought after 9/11 it was a two-year project. We know now 9/11 was closer to five years in the making.”

At the White House, Bush’s counterterror chief, Frances Townsend, chairs a daily 9 a.m. videoconference of senior staffers at the CIA, the FBI and the new Terrorist Threat Integration Center, known as TTIC. Officials speak of multiple “threat strands” and “the retail structure” of very loosely affiliated groups. In his recent testimony, Tenet talked of “a global movement infected by Al Qaeda’s radical agenda” and said “the steady growth of bin Laden’s anti-American sentiment and the broad dissemination of Al Qaeda’s destructive expertise ensure that a serious threat will remain for the foreseeable future, with or without Al Qaeda in the picture.” A senior U.S. intelligence official adds: “Everyone is looking for neat explanations, but unfortunately the terror-threat assessment is much messier. Al Qaeda is on the run, but it is not vanquished. The problem is, we simply don’t know what it is capable of pulling off.”

What is known is that terror cells of various kinds riddle the Middle East, Europe, Africa and parts of Southeast Asia. Some are still comfortably situated in friendly nations. The former leader of an alleged Qaeda affiliate in Iraq called Ansar al-Islam, a fiery jihadist preacher known as Mullah Krekar, still lives openly in Norway. Under U.S. pressure–including a visit last year to Oslo by Attorney General John Ashcroft–Norwegian authorities have repeatedly tried to lock him up, only to see the courts release him for insufficient evidence. Switzerland, too, is only just discovering its role as a terror way station. Swiss investigators initially played down reports that 9/11 hijacker Muhammad Atta once transited Zurich in connection with a visit to Spain, and that suspected “dirty bomber” Jose Padilla visited Zurich twice between fleeing Afghanistan and traveling to America (where he was arrested). But a few weeks ago, the Swiss picked up eight Muslim men on suspicion they were involved in helping Al Qaeda stage the attacks last May against residential compounds in Riyadh. The Muslim regions of Africa are also increasingly regarded as rich recruiting grounds. In several places–Sudan, across the Sahara’s ancient caravan routes to Nigeria and Mauritania, even in South Africa–elements of Muslim communities are becoming radicalized. And a bit of bribe money can take a fugitive from one end of the continent to the other.

International investigators are deeply divided on how big a presence the old Qaeda still is in the new-generation network–in other words, how much the budding terror groups merely coexist with it as opposed to taking orders. In Washington, officials tend to consider bin Laden mainly a symbolic presence now, especially as the U.S. military has just begun what many consider its final push to get him, launching Special Forces and units in Afghanistan and Pakistan last week. Foreign governments tend to believe that bin Laden and Zawahiri are more operationally active and in charge. The Saudi ambassador to London, Prince Turki al-Faisal, says that officials in Saudi Arabia believe that terrorists who committed bombings there last spring were “definitely taking orders” from bin Laden. In Turkey, investigators also believe that the perpetrators of recent bombings were affiliates of Al Qaeda.

Questions about the alleged relationship between Zarqawi and bin Laden illustrate this debate. In the letter allegedly written by Zarqawi or his subordinate, carried by a man named Hassan Ghul, the writer defers to Al Qaeda as the lead group: “You, noble brothers, leaders of Jihad, we do not consider ourselves those who would compete against you…” But some analysts have argued that, instead of addressing Qaeda leaders as a supplicant or subordinate, the writer seems to be speaking to them as an equal. Even when he was in Afghanistan, Zarqawi had his own operation, a terror camp in the Afghan city of Herat.

Within U.S military intelligence, current opinion is that Zarqawi has maintained a significant degree of independence from Al Qaeda. And some U.S. intelligence officials now believe there is a serious and fundamental doctrinal split between what is left of the Qaeda leadership and Zarqawi. The latter, if his alleged memo is to be believed, thinks that killing fellow Muslims is a legitimate tactic in a long-term campaign to drive the United States and other infidels out of holy Muslim lands, whereas bin Laden is said to oppose that in principle.

After all the attacks, from New York to Baghdad to Madrid, this much is painfully clear: the threat is spreading over a wider and wider area. It’s noteworthy that in the letter found on Ghul, the writer suggested that if the terror campaign failed in Iraq, the group could simply “pack up and go somewhere else.” That’s the sort of philosophy that once allowed Al Qaeda to be as deadly as it was–and that could make its successors equally frightening long after Al Qaeda is gone.