Yet none of those cities is in China. Shen Yun, whose three touring groups are composed of mostly ethnic Chinese from around the world, is based in New York — and steeped in certain aspects of traditional culture that have been suppressed under China’s Communist regime.

Shen Yun, which translates as Divine Performing Arts, was established in 2006 by a group of artists trained in classical Chinese dance and music. “They came together with the mission of revitalizing traditional Chinese culture,” said Levi Browde, the manager for Shen Yun promotion in Westchester and a spokesman for New Tang Dynasty Television, which is presenting the company at Purchase. “They do this through the art forms themselves — the leaps and tumbles and spins — and through the stories that those art forms tell.”

Those stories include the legends of Yue Fei, the Song dynasty general revered for his loyalty, and Mulan, the heroine who joined the army disguised as a man. There is a retelling of a Buddhist monk’s pilgrimage to India, derived from the 16th-century Chinese novel “Journey to the West,” as well as modern tales like “Astounding Conviction,” focusing on the spirit of a peaceful demonstrator arrested in Tiananmen Square.

Each year, the company presents an original production. The two-and-a-half-hour show at Purchase’s Performing Arts Center combines elaborate choreography, original compositions, ornate costumes, fanciful props and animated backdrops in about 20 vignettes that range from solo performances to full ensemble acts. Thirty dancers moving in synchronized patterns to re-enact a fable from ancient China may be followed on stage by a lone musician playing the erhu, a two-stringed instrument that dates back 3,500 years.

Other segments feature operatic singing, drumming and folk dances from Tibet, Mongolia and other border regions. Before each act, two M.C.’s — a man and a woman — present a brief introduction in English and Chinese, with plot summaries and background information.

The performers are accompanied by an orchestra that combines Chinese instruments, like the stringed pipa, the guzheng (sometimes called the Chinese zither) and the bamboo flute, with Western instruments. “This is technically difficult,” Mr. Browde said, “because the tonalities are so different.”

Every piece is set against a different digital backdrop: scenes of palaces, grasslands, mountains, snowfalls and clouds, all animated and coordinated with the performers’ movements.

“In one performance, a dancer shoots an arrow into the air, and you see it moving through the background,” Mr. Browde said. “In another, the figures in an animated battle scene interact with the dancers onstage.”

A nonprofit group supported by ticket sales and donations, Shen Yun began as a single company of 30 dancers. During its inaugural season in 2007, its 32 performances were seen by 200,000 people. The company’s second date at Purchase, in September, will close its 2010 season, which has reached over a million people.

Shen Yun has more than 200 members who travel and perform seven months a year. In addition to award-winning dancers and musicians, each of the three companies has its own orchestra, choreographers, composers, M.C.’s, costume and set designers, backdrop and computer artists. All are trained at Shen Yun’s headquarters in Cuddebackville, in Orange County, N.Y., taking their cues from traditional Chinese teachings.

“They believe that to be a phenomenal artist, you can’t just learn phenomenal technique,” Mr. Browde said. “You have to live a certain lifestyle. You have to be strong. You have to be calm. You have to be compassionate. You have to be at peace with yourself. Those qualities, whether visible or not, come through you — and people will feel them.”