Train a cat to quit scratching the furniture? Sometimes works. To come when you call him? Only when he feels like it.

But to do a handstand—er, paw-stand—before hundreds of cheering strangers? Only in the Moscow Cats Theatre, a troupe of 26 nimble felines performing eye-popping acro-catics—from pushing baby strollers to scooting across tightropes. The show, which also features colorful skits performed by four clowns and one unlucky dog, is playing to frequently sold-out crowds during its U.S. debut in New York City. Their run has recently been extended to December, and plans are afoot for the four-legged stars to move to a bigger Off-Broadway theater next year.

Not bad for a cast of cats who can't sing "Memory." Instead, Cats Theatre founder Yuri Kuklachev, 56, cultivates his charges' natural talents. "I watch the cats when they are 2 or 3 months old and I see what they can do," says Kuklachev, who rents a three-bedroom apartment in Brighton Beach, Brooklyn, for his furry friends (he shares the space above with his wife and fellow clown, Yelena, 55). "One might like to climb a tree, so I use him to climb a pole." But how does he get them to perform on cue? "I hug them," he says. "I say, I love you, you are the prettiest.' " If all else fails, Kuklachev resorts to a trick of his own: treats. "They love chicken."