Carla Maxwell, a dancer and choreographer who led the José Limón Dance Company for nearly 40 years, forging a path for how modern dance troupes can endure beyond the death of their founders, died on Sunday in Manhattan. She was 79.

Her nephew, Omar Guerrero, confirmed her death, at a nursing home, but did not specify a cause.

When Ms. Maxwell became artistic director of the Limón company in 1977, few people expected her to last very long. Mr. Limón had died five years earlier, and no other major modern dance company had survived after its founder had died.

Like Martha Graham, Mr. Limón was the star dancer and principal choreographer of his namesake troupe. Appraisals after his death recalled the brooding charisma and moral certitude of his stage presence and ranked him as one of America’s greatest choreographers. What was the Limón company without its creator and guiding force?

“We not only had to prove that we could survive,” Ms. Maxwell said in an interview for the 2001 documentary “Limón: A Life Beyond Words.” “We had to prove that José’s work was worth maintaining.”

Ms. Maxwell, who had joined the company as a dancer in 1965, made her argument through action. Preserving company staples while also regularly reviving neglected or lost Limón works and importing and commissioning works by other choreographers, she attracted dancers, audiences and funders. This became a model for other companies, like Graham’s, after their founders died.

The inclusion of works by choreographers other than Mr. Limón was not a break with company history. Born in Mexico to parents who migrated to Los Angeles, Mr. Limón was the protégé of the choreographer Doris Humphrey, who, alongside Graham, had emerged from the school and company of Ruth St. Denis and Ted Shawn. Mr. Limón became the lead male dancer of the company that Ms. Humphrey shared with Charles Weidman, and when he decided to found his own troupe, in 1946, he took the unusual step of asking Ms. Humphrey to serve as artistic director.