John Stamos claims he once caught a girlfriend of his in the '80s cheating with Tony Danza ... a revelation he's making in a new book he's got coming out.

The actor makes the allegation in his forthcoming memoir, "If You Would Have Told Me," an excerpt of which Entertainment Weekly got their hands on -- detailing this juicy tale. According to JS, he says the alleged affair took place between Danza and Teri Copley.

Stamos says this all went down in the mid-'80s when he was dating Copley ... whom he says he was madly in love with. About a year into their relationship, he says he noticed a change in her while he was out on the road doing gigs (this was pre-"Full House," mind you).

He says he felt like she was becoming dodgy and not returning his calls, so one day ... Stamos swung by her place to see what was up, which is where he says he discovered Tony passed out in Teri's bed -- butt ass naked, at that ... at least TC was, anyway.

Long story short, John says he found Tony's vintage Porsche in the parking lot of Teri's apartment -- but didn't realize who it belonged to at first. JS says he made his way inside Teri's home -- the door to which he says was cracked open -- and that's where he saw his GF in bed with a dude, both of them asleep. John describes it as his "worst nightmare."

As he started to leave, John peeked into the guy's car again and saw a poster featuring Teri half naked -- which she'd signed for the fella, writing ... "My Dear Tony, I'll love you forever. XO, Teri." John says it eventually hit him on who it was ... "Hold me closer, Tony Danza."

Of course, Tony was huge in the '80s with his starring role in "Who's The Boss?" -- and Teri was doing a different sitcom at the time as well ... "We Got It Made." Safe to say, Stamos ended things with Teri after that. Neither Danza nor Copley have responded to the story.