All cats have a special name and a secret life that humans will never understand.

That was the message that the Fourth National Touring Company of the musical “Cats” offered during five shows at Portland’s Merrill Auditorium over the weekend.

The musical by Sir Andrew Lloyd Webber is based on T.S. Eliot’s fanciful “Old Possum’s Book of Practical Cats.” It tells the story of a tribe of Jellicle cats, who come together once a year at the Jellicle Ball to select one cat to ascend to the Heaviside layer, there to be given the chance to live another life. As the show progresses, different cats, candidates for ascension, are introduced and their stories are told.

“Cats” is the longest-running musical in Broadway history, and not coincidentally, the Fourth National Touring Company is the longest-running individual touring company in history, as it’s been on the road since 1987.

So at the Saturday matinee, the sellout crowd got to enjoy a production polished to a bright sheen over time. It didn’t take long for the “Cats” cast to prove they were more than just another touring company trekking to Maine.

As the musical begins, cats’ eyes flash all around the garbage dump, which is the Jellicles’ gathering spot. The oversized household items in the trash-heap set design created by John Napier and reproduced by Raymond Huessy help to bring the audience in to the cats’ stomping grounds immediately.

The actors come in on little cats’ feet, silently, carefully. But once they’re sure there are no humans around, they’re soon leaping, around the set and across the stage. “Cats” is a movement-intensive musical, and the youngish cast is certainly up for all the dancing involved in the show.

The distinctive makeup, costumes and yak-hair wigs designed originally by Napier, let the audience see cats’ ears and whiskers, even where none actually existed. The colorful look is part of what makes the musical accessible even for young children.

“Cats,” which is songs from beginning to end with no dialogue per se (although there is speak-singing), is filled with showcase numbers, which gives individual actors an opportunity to shine.

Andy Karl is a real scenery-chewer as Rum Tum Tugger, the rock ‘n’ roll cat, who sneers, swaggers and pelvic-thrusts his way around the dump, to the screams of all the female kittens, both during his self-titled song in the first act and “Mr. Mistoffelees” in the second act. Even when he was in the background, Karl’s Rum Tum Tugger stood apart and stood out.

Another standout was Jennifer Hughes as Jennyanydots, featured in “The Old Gumbie Cat.” Jennyanydots is a roly-poly cat who appears most at home lying in front of a fire. But at night, she teaches self-improvement courses to mice and cockroaches, and she also does a mean tap-dance.

But perhaps the cast’s most gifted dancer is Julius Sermonia as the magical Mr. Mistoffelees. Dressed in black, Sermonia flew about the stage, and drew applause from the audience for an extended pirouette during his self-titled number.

Making the most out of a featured but less-showy role was Jodie Langel as Grizabella, the former glamour cat now shunned by the rest of her tribe. Langel’s Grizabella showed her pain and regrets about her lost youth and innocence in renditions of the oft-copied “Memory” in both acts, displaying a dynamite voice at the same time.

All told, the Fourth National Touring Company showed the Portland audience why “Cats” has become an enduring classic of modern theater, and left many wishing that such productions would come more regularly to Maine.