The mastermind of the 9/11 attacks, Khalid Shaikh Mohammed, would later claim to C.I.A. interrogators that he sent the two men to Los Angeles without any contacts at all — an assertion that both the 9/11 Commission and Danny Gonzalez found improbable. Neither Saudi spoke English. What little they knew about life in the West came mostly from a crash course in Pakistan, in which Mohammed tried to teach them to read airline timetables and telephone books and showed old Hollywood movies with hijacking scenes. Documents from the investigation show that even Mohammed doubted they could get the job done.

But, after gathering their duffel bags and clearing customs at LAX, Mihdhar and Hazmi managed to disappear. If closed-circuit cameras followed them through the airport’s international terminal, or if anyone came to meet them, no recording has ever surfaced publicly, and F.B.I. agents on the case said they did not see one. When F.B.I. agents canvassed dozens of hotels around Los Angeles, they found no evidence that the Saudis stayed at any of them during those first two weeks. In its detailed report on the plot, the 9/11 Commission wrote simply, “We do not know where they went.”

On orders from the F.B.I.’s new director, Robert S. Mueller III, Penttbom set up its command center in a poorly lit room in the basement of the J. Edgar Hoover Building in Washington, where the F.B.I. is headquartered. Various teams — including one for each hijacked flight — coordinated the work of agents around the country. It was an unusual arrangement, one that limited the autonomy of the field offices to run their own cases. Counterterrorism agents often complained before 9/11 that headquarters tightly managed the flow of intelligence information, sometimes to the detriment of investigations. Now, in the biggest case the F.B.I. had ever undertaken, that kind of control became standard practice.

In the months after the attacks, the harried Penttbom teams logged more than 250,000 leads, most of them insignificant. But a number of clues suggested Saudi involvement: A Saudi engineering student was among the Arizona extremists reported by Williams before the attacks; in March 2002, the student was captured with Qaeda bomb makers in Pakistan. Two other Saudis associated with the Arizona group were briefly detained in 1999, after one of them tried to enter the cockpit during a flight from Phoenix to Washington for an event at the Saudi embassy. Airline officials eventually apologized to the men, but some investigators later came to suspect that they had carried out a dry run for the 9/11 hijacking plot. A Saudi woman in San Diego, a close friend of Bayoumi’s wife, received about $70,000 in payments from the wife of Prince Bandar, then the powerful Saudi ambassador to the United States. Although initially intrigued, Washington investigators eventually concluded that the vastly wealthy Bandars often gave money to Saudi expatriates.

But even as the flurry of Saudi-related clues continued, Gonzalez and other agents began to note some skepticism within the F.B.I. hierarchy about the idea that the Saudis were linked to the case. In September 2002, Lambert, the counterterrorism chief in San Diego, was asked to help prepare Mueller’s testimony to a joint inquiry of the House and Senate Intelligence Committees that had been established to investigate intelligence failures leading up to the attacks. Mueller’s deputy, Bruce Gebhardt, explained how Lambert was to describe the Saudi role. “The bureau’s position is that there was no complicity” in the plot, Lambert recalls Gebhardt telling him. (Gebhardt says he does not remember the exchange.)

Lambert was struck by the decisive conclusion being drawn on a question he thought was far from settled. But he realized no one wanted his opinion. “I had my marching orders,” says Lambert, who is now consulting for the lawyers to the Sept. 11 families. “It was very apparent to me that that was a decision that was made at a very high level, and that’s what I wrote to.”

Parts of Mueller’s testimony on Sept. 26, 2002, remain secret, and there is no indication in the public record that he exonerated any Saudis suspected of involvement in the plot. Still, he played down the idea that the hijackers had any established support network in the United States or should have drawn F.B.I. scrutiny. “While here, the hijackers effectively operated without suspicion, triggering nothing that alerted law enforcement,” he said.