Through the early 1970s, Mr. Forman — a hearty bon vivant without means for the good life at the time — went through a period of self-described depression. For much of that time he holed up in the storied Chelsea Hotel in Manhattan, sleeping through the days and communicating with émigré friends.

By then he had been married twice, first to an actress, Jana Brejchova, then to another performer, Vera Kresadlova, who had remained in Czechoslovakia with their two sons, Petr and Matej.

In addition to those sons, he is survived by Martina Formanova, his third wife; and his twin sons, James and Andrew, with Ms. Formanova.

In his memoir, Mr. Forman said the producers of “Cuckoo’s Nest,” Michael Douglas and Saul Zaentz, sought him out because “I seemed to be in their price range.” In fact, they had made a prudent match between filmmaker and material, the Kesey novel.

Jack Nicholson was the movie’s star. But Mr. Forman — who liked to coax star performances out of lesser-known actors — did exactly that with Louise Fletcher, who won an Oscar for her portrayal of the dictatorial Nurse Ratched.

“Hair,” a 1979 adaptation of the counterculture Broadway musical, and “Ragtime,” which came next, in 1981, a film version of the E. L. Doctorow novel, with James Cagney, left less impression. But they kept Mr. Forman on the list of directors whom executives were willing to trust with more sophisticated projects.