Donny and Marie Osmond love what they do. They’ve said it many times before when asked about the secret of their longevity as performing partners, how they approach their Las Vegas show with as much enthusiasm and energy as they did as teenage variety show superstars, and how they’ve managed to turn a six-week engagement at the Flamingo in 2008 into a nearly decadelong run. In September, the siblings will observe the 10th anniversary of the residency, a production structured not all that differently from the weekly broadcast on ABC from 1976 to 1979.

Donny and Marie Osmond’s legacy as entertainers dates back far longer than that, though. Both appeared on singer Andy Williams’ television show in the ’60s. Williams had been regularly featuring their older brothers Alan, Wayne, Merrill and Jay after Walt Disney first discovered them harmonizing at his theme park and cast them in a televised special. Williams, who co-headlined the Flamingo with comedian Joe E. Lewis in 1957, brought Donny on at age 5 to sing a jazzy version of “You Are My Sunshine,” while Marie made her debut on the program at age 3.

The Osmonds would rocket to superstardom in the early ’70s, charting hits such as “Yo-Yo” and “Crazy Horses” that Donny delivers during his set. He also sings “Puppy Love,” a hit for him at 13, which launched his solo career and made him a top teen idol. The momentum transferred to television. Marie became an overnight star after the debut of Donny & Marie, where she first sang a medley with her brother that begins with “It Takes Two” and could lead anywhere in the pop, rock or country universes. It’s the song they start their show off with today.

While their fans may find themselves transported back to a time when Donny and Marie were peaking as youthful entertainers, their subsequent solo careers also inspire the show. Marie, who achieved her first chart hit at age 13 with “Paper Roses,” focused on country music in the ’80s, appeared on Broadway and developed her operatic chops. She shows them off during the show, along with her interpretation of 25 iconic faces during a video segment that has her made up like Elizabeth Taylor and many others.

Donny would go on to play the title role in Broadway’s Joseph and the Amazing Technicolor Dreamcoat, which is represented during his set along with his contribution to Disney’s Mulan, “Let’s Get Down to Business,”  and his 1989 comeback hit “Soldier of Love.” He also gets ample opportunity to demonstrate the dancing skills that led to his victory during the 2009 season of Dancing with the Stars. A live band, biographical video, and trademark all-in-fun bickering add to the elements that have made Donny and Marie’s residency a hit for nearly a decade. By all appearances, it looks like they might have a home at the Flamingo for years to come.

Flamingo, 7:30 p.m. Tues.-Sat. , $95-$260 plus tax and fee. 702.777.2782