Officers of the associations, who are vetted and sometimes chosen by the Cultural Mission, report to it on meetings, activities and social media posts from other students, especially anything that might suggest Islamist militancy or criticism of the Saudi regime. Counterintelligence experts said the system resembles the approach used by China to spy on its students overseas.

"The student associations are an important part of the mechanism of control," said Abdullah Alaoudh, a fellow at Georgetown University's Center for Christian-Muslim Understanding, who was stripped of his Saudi government scholarship while studying law at the University of Pittsburgh. "That's who denounced me for being a dissident. They report on you to the Cultural Mission, and the mission had a file on me with all my Twitter and Facebook posts."

Nazer, theSaudi Embassy spokesman, said that the cases of students who have broken American laws represent "clear aberrations" among the hundreds of thousands of Saudis who have studied productively in the United States since the 1960s. He insisted they are not "a reflection on the large Saudi student population in the country, the overwhelming majority of which is law-abiding."

In a number of cases since 2002, current and former officials said, FBI agents began investigating visiting Saudis for possible extremist ties only to have the visitors disappear. The Saudi government had gotten there first, possibly after conducting its own surveillance of social media platforms, or being warned by its student network, or becoming aware of the bureau's surveillance.

One former federal law enforcement official described a 2014 incident in which a