WASHINGTON (AP) - Senators are hearing closed-door testimony this week about an allegation of sexual misconduct against Air Force Gen. John Hyten as they weigh his nomination for vice chairman of the Joint Chiefs of Staff.

A senior military officer who has accused Hyten of unwanted sexual advances met Tuesday with senators from the Armed Services Committee in a classified setting. Hyten, who was nominated for the post in April, is expected to appear for another classified executive session at the committee Thursday.

The committee chairman, Sen. James Inhofe, R-Okla., said he was hopeful of moving forward with a vote in the committee possibly next week, before the Senate recesses for August.

“We’re still aiming to get this done,” Inhofe said. “I am personally interested in moving forward with him after we have an executive session.”

Other senators, though, have raised questions about the situation and are insisting on more information. Several senators pressed for this week’s classified briefings. The general’s nomination has lagged for months and it is unclear if Hyten has enough support to be confirmed.

Sen. Richard Blumenthal of Connecticut, a Democrat on the committee, has said both Hyten and the alleged victim need to be heard.

After Tuesday’s classified briefing, he said she had “raised very serious allegations.” He said, “They need to be very closely and carefully considered.”

Inhofe confirmed that Hyten was expected to appear later this week, likely Thursday, and that the committee could have a public session next week.

The prospect of a full committee session could prove politically challenging as President Donald Trump’s nominees have faced a grilling over their personal and professional behavior, especially at a time of heightened awareness of sexual misconduct in the “Me Too” era.

The Associated Press reported on the allegations against Hyten earlier this month.

The officer told AP that Hyten subjected her to a series of unwanted sexual advances by kissing, hugging and rubbing up against her in 2017 while she was one of his aides. She said that he tried to derail her military career after she rebuffed him.

The Air Force investigated the woman’s allegations, and found there was insufficient evidence to charge the general or recommend any administrative punishment. The accuser remains in the military but has moved to a different job.

The woman asked to not be identified by name. The AP generally does not identify those who say they have been sexually assaulted.

The accusations came at a time of unusual turmoil in the top ranks at the Pentagon. On Tuesday, the Senate confirmed Mark Esper as defense secretary, filling a role that had only an acting chief for the past six months. Then-Secretary James Mattis stepped down and Trump’s nominee to replace him, Patrick Shanahan, withdrew after revelations about his contentious divorce.

The uncertainty around Hyten’s nomination leaves another potential opening. The current vice chairman, Gen. Paul Selva, is scheduled to retire at the end of the month. If Hyten is not confirmed by the Senate by then, there will be a vacancy.

Inhofe, who has not said how he will vote on Hyten, said shortly after the accusations surfaced publicly this month they are “totally out of character” from the general’s background.

The chairman said he has been twice briefed on the matter, once with the top Democrat on the committee, and again with the full committee earlier this month.

Inhofe has said he cannot recall a “more thorough” investigation than the one the military did that found no evidence of wrongdoing, a position he maintained after Tuesday’s session.

“I don’t recall a better run, more thorough investigation,” he said. “I still believe that.”

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