The psychologists were called by lawyers to testify for one of the defendants, Mr. Mohammed’s nephew, Ammar al-Baluchi. All five defense teams are expected to question them about policy and for graphic details of conditions in the clandestine overseas prisons, including one in Thailand that for a time was run by Gina Haspel, now the C.I.A. director.

Mr. al-Baluchi’s lawyer, James G. Connell III, is spearheading an effort to persuade the judge to exclude from the trial the testimony of F.B.I. agents who questioned the defendants at Guantánamo in 2007. It was just months after their transfer there from years in C.I.A. prisons, and the defense lawyers argue that, although there was no overt violence during the F.B.I. interrogations, the defendants were so thoroughly broken in the black sites that they were powerless to do anything but tell the F.B.I. agents what they wanted to hear.

By law, prosecutors can use voluntary confessions only at the military commissions at Guantánamo.

Dr. Mitchell has described waterboarding and other violence as well as sleep deprivation and forced nudity as part of a program of “conditioning” captives to cooperate that has no long-lasting effect on them.

Dror Ladin, a lawyer with the American Civil Liberties Union, called the circumstances of the testimony “very strange” and “very extraordinary.”

He said “torture survivors,” the Sept. 11 defendants, will be watching “the men who tortured them testify as witnesses in a trial that will decide whether the defendants will be put to death in part based on the testimony of the very same people who tortured them.”

Mr. Ladin was part of a legal team that filed a civil lawsuit and then reached a confidential settlement with Dr. Mitchell and Dr. Jessen on behalf of three foreign men who were held in a C.I.A. prison in Afghanistan and interrogated using some of the methods they drew up. One of them died in custody.

Dr. Mitchell said at the time that it was “regrettable that one guy died and those other guys were treated badly.” But he said he and Dr. Jessen “were not responsible for it.”