Michael Douglas talked for the first time about his cancer Tuesday night on 'The Late Show with Dave Letterman.' The actor told the audience he's in the middle of an "eight-week struggle" against throat cancer but is hopeful about his chances for recovery.

Douglas revealed that he was diagnosed three weeks ago, though he'd complained of a sore throat and ear pain at one point earlier this year. Testing at the time didn't find a cause for the discomfort. When he returned to the doctor after a summer of traveling with wife Catherine Zeta-Jones and their two kids, Dylan Michael and Carys Zeta, he was diagnosed with stage-four cancer, "which is intense, and so they've had to go at it," he said.

"It makes me furious they didn't detect it earlier," Zeta-Jones told PEOPLE. "He sought every option and nothing was found."

When the actor revealed to Letterman that he'd just finished his first week of radiation and chemotherapy, the talk show host was visibly surprised. "You've never looked better to me, and this proves that you're a tough guy, for God's sakes," Letterman said.