By PATRICK HEALY

Stars and celebrities have become crucial to modern Broadway, with virtually every top-grossing play and many musicals having household names in the cast. But Broadway’s dependence on star casting has a decided downside: how do you recast roles that grow to be heavily identified with widely recognized actors? Often they come from television, like Sean Hayes, the star of Broadway’s $9 million revival of “Promises, Promises,” which will close in January when he and his co-star, Kristin Chenoweth, leave the show.

The pair are the chief reasons the show usually grosses $1 million a week. Among the hits of the last Broadway season were the drama “Fences,” with Denzel Washington, and the musical “A Little Night Music,” with Catherine Zeta-Jones, both Oscar winners. “Fences” was revived for Mr. Washington and closed when he left. When Ms. Zeta-Jones departed “Night Music” in June, the weekly box office grosses promptly fell by 40 percent, and have only crept up since, thanks to the rave reviews for Ms. Zeta-Jones’s replacement, Bernadette Peters.

The concern about replacing a star, or two, is what could be called the “Producers” syndrome, after the fate of the 2001 musical “The Producers”: the show was a mammoth hit starring Nathan Lane and Matthew Broderick; when they left after a year, advance ticket sales declined sharply .

The producers of one current hit musical, “The Addams Family,” deliberately played down the star actors in their advertising and logos. The producers emphasized the cartoon characters made famous in the pages of The New Yorker magazine - hoping to make it easier for actors to slide into the lead roles now held by the show’s popular stars, Mr. Lane and Bebe Neuwirth, who are expected to leave the production in March. Even so, the producers are furiously seeking stars to replace its star lead s .

It is clear that Mr. Lane and Ms. Neuwirth have become essential to ticket sales. When Mr. Lane took a week’s vacation from the show in July, the weekly grosses slid to $764,231 from $1.1 million. Ms. Zeta-Jones’s vacation from “Night Music” in February caused a similarly intense box office chill. Some producers firmly believe that when they refill a role, they have to “cast up” ? finding a new actor who is an even bigger name than the original.

This can be a problem when the original is already a star. The producers of “Night Music” opted for a big name in theater circles, Ms. Peters, rather than try to find an even bigger screen star than Ms. Zeta- Jones. (“Night Music” has earned back its original costs.) The producers of the play “Race,” meanwhile, went from the American television star James Spader to a British replacement, the actor and comedian Eddie Izzard, in June. The grosses ended up dropping roughly 30 percent before the play closed, as planned, in August.

“The challenge is if you started with a star, you’re stuck, because you’re always going to need a star,” said Jeffrey Seller, a lead producer of the current “West Side Story” revival and “In the Heights.” Tom Viertel, a lead producer of “The Producers,” recalled that he and his partners convened a focus group to discuss “re-imaging” the musical as Mr. Lane and Mr. Broderick were preparing to leave.

The advertising had been built around the pair’s rubbery faces , and they had to come up with images that would newly excite theatergoers. “There were ads that included chorus girls, that highlighted our Tony Awards, that had Cady Huffman lying on her side,” Mr. Viertel recalled. “We never really fixed on one image, in the end. We kept changing it up over the six-year run.” Beth Williams, a lead “Promises, Promises” producer, said her team had “ didn’t think there was a way to replace Sean and Kristin” and ensure extending the show’s financial track record as well.

The musical has grossed more than $27 million since opening in April. Casting new leads for the show could cost at least $100,000 in rehearsal time, advertising and other expenses. The production received mixed reviews from critics, and won only one Tony Award in June, for Katie Finneran, a supporting actress. Discussions about new casting never reached the point of talking to actors or their agents about joining “Promises.”

Ms. Williams declined to provide the names of anyone she was mulling over as replacements. “My dream casting,” she said, “would be for Sean and Kristin to extend for another year.”