NEW YORK — George Wendt, an actor with an Everyman charm who played the affable, beer- loving barfly Norm on the hit 1980s TV comedy “Cheers” and later crafted a stage career that took him to Broadway in “Art,” “Hairspray” and “Elf,” has died. He was 76.

Wendt’s family said he died early Tuesday, peacefully in his sleep at home, according to the Agency Group publicity firm.

Despite a long career of roles onstage and on television, it was as gentle, henpecked Norm Peterson on “Cheers” that he was most known, earning six straight Emmy nominations for best supporting actor in a comedy from 1984 to 1989.

The series was centered on lovable losers in a Boston bar and starred Ted Danson, Shelley Long, John Ratzenberger, Rhea Perlman, Kelsey Grammer, Kirstie Alley and Woody Harrelson. It was nominated for an astounding 117 Emmy Awards, winning 28.

Wendt, who spent six years in Chicago’s renowned Second City improv troupe before sitting on a barstool at the place where everybody knows your name, didn’t have high hopes when he auditioned for “Cheers.”

“My agent said, ‘It’s a small role, honey. It’s one line. Actually, it’s one word.’ The word was ‘beer.’ I was having a hard time believing I was right for the role of ‘the guy who looked like he wanted a beer.’ So I went in, and they said, ‘It’s too small a role. Why don’t you read this other one?’ And it was a guy who never left the bar,” Wendt told GQ in an oral history of “Cheers.”

“Cheers” premiered on Sept. 30, 1982, and spent the first season with low ratings. But it was nominated for an Emmy for best comedy in its first season. Some 80 million people would tune in to watch its series finale 11 years later.

Wendt became a fan favorite — his entrances were cheered with a warm “Norm!” — and his wisecracks always landed. “How’s a beer sound, Norm?” the bartender would ask him. “I dunno. I usually finish them before they get a word in,” he’d respond.

After “Cheers,” Wendt starred in his own short-lived sitcom, “The George Wendt Show” — “too bad he had to step out of Norm and down so far from that corner stool for his debut stanza,” sniffed Variety — and had guest spots on TV shows like “The Ghost Whisperer,” “Harry’s Law” and “Portlandia.” He was part of a brotherhood of Chicago Everymen on “Saturday Night Live” who gathered over sausage and beers and adored “Da Bears.”

But he found steady work onstage: Wendt slipped on Edna Turnblad’s housecoat in Broadway’s “Hairspray” beginning in 2007 and was in the Tony-winning play “Art” in New York and London.

He starred in the national tour of “12 Angry Men” and appeared in a production of David Mamet’s “Lakeboat.” He also starred in regional productions of “Death of a Salesman,” “The Odd Couple,” “Never Too Late” and “Funnyman.”

Born Oct. 17, 1948, in Chicago, Wendt attended Campion High School, a Catholic boarding school in Prairie du Chien, Wisconsin, and then Notre Dame, where he rarely went to class and was kicked out. He transferred to Rockhurst University in Kansas City and graduated after majoring in economics. He found a home at Second City in the touring company and the mainstage.

“I think comedy is my long suit, for sure. My approach to comedy is usually not full-bore clownish,” he said. “If you’re trying to showboat or step outside, it doesn’t always work. There are certain performers who almost specialize in doing that, and they do it really well. But that’s not my approach.”

He is survived by his wife, Second City alum Bernadette Birkett, who voiced Norm’s never-seen wife, Vera, on “Cheers”; his children, Hilary, Joe and Daniel; and his stepchildren, Joshua and Andrew. “Ted Lasso” star and co-creator Jason Sudeikis is a nephew of Wendt.