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Mr. Thompson said that the university reviewed all its courses a year ago, as mandated by the White House. It sent a December 2011 memo to the Joint Staff vouching for its courses and mentioned the need for academic freedom.

“Everything he had done up to this point had the approval of the chain of command of the National Defense University, and he had gotten the highest marks as an instructor,” Mr. Thompson said. “All the external instructors had been pre-approved before he used them.”

The Army this month transferred Col. Dooley from the university to the nearby Army Capabilities Integration Center, where he is chief of the lethality branch.