The rewards have become significant for American producers. They typically receive 15 percent of the box office gross, as well as licensing and management fees in some cases, revenue that can total millions of dollars and offset losses on Broadway.

And they see South Korea as a model for eventually doing business in an even bigger future market, China.

Ask Edward Strong, a partner in Dodger Theatricals, which is bringing another unmistakably American musical, “Jersey Boys,” to Seoul for the first time in January as part of an English-language tour.

“All of Asia is a potential market for ‘Jersey Boys,’ ” he said. “But right now, Seoul is the major market, ever since the economic recession cooled theater activity in Japan. And we want to learn from our experience in Seoul and take that knowledge elsewhere in Asia.”

The strong business from young women (and plenty of young men too) is generally attributed to the fact that Koreans in their 20s and 30s tend to earn good salaries but live with their parents until marriage. This leaves them money to spend on tickets, which cost roughly the same as in New York.

Ticket sales began to climb for American and British musicals after the unexpected success of a Korean-language version of “The Phantom of the Opera” in 2001, according to Korean producers. “Phantom” ran for seven months, a relatively long run here; most popular musicals run for a few months, shut down, then return a year or two later. Rotating like this allows fresh celebrities to be added to the casts, which fuels repeat business; stars from popular K-pop bands routinely sell out their performances and can earn as much as $50,000 a night in a musical.