NEW YORK (AP) – Michael Douglas says he faces an “eight-week struggle” against throat cancer but is optimistic about his chances for recovery.

During an appearance Tuesday on David Letterman’s “Late Show,” the actor said he had just finished his first week of radiation and chemotherapy.

That drew a surprised reaction from Letterman.

“You’ve never looked better to me, and this proves that you’re a tough guy, for God’s sakes,” the talk-show host said, drawing cheers from the studio audience, according to a CBS news release.

“Let’s just say ... I’m pretty lit up right now,” Douglas replied.

The disease was diagnosed three weeks ago, he said, although he had complained of a very sore throat earlier this year and had undergone testing that failed to find a cause.

Douglas, 65, who has two children with Catherine Zeta-Jones, said he enjoyed the summer traveling with his family before returning to the doctor.

A biopsy found he had late, stage-four cancer, “which is intense, and so they’ve had to go at it,” he said.

However, Douglas said, the cancer remains above the neck and that means expectations are good, with an 80 percent or better chance of recovery.