Mr. Hackman did end up learning the Method, not from Mr. Strasberg but from George Morrison, his original director in the 1964 Broadway production of ''Any Wednesday.'' Mr. Morrison was fired in rehearsals when the producers thought he was taking too much time laying the psychological foundation for what was supposed to be a breezy boulevard comedy. But Mr. Hackman felt those foundations enabled him to take big risks onstage for the first time. He sought out Mr. Morrison for private instruction, and credits him for relaxation techniques that he practices to this day. Mr. Morrison also taught him to ask two fundamental questions about every part: ''How am I like this person?'' and ''How am I not like this person?''

A characteristic Hackman motif is visible, in embryo, in his first significant film part, in Robert Rossen's ''Lilith'' (1964). In his only scene, Mr. Hackman greets Warren Beatty with a hick geniality out of which oozes, slowly but with increasing intensity, a stream of bile. Mr. Hackman gives the only grounded performance in the movie -- an opinion shared by Mr. Beatty, who would tap him, three years later, for his breakthrough role as Buck Barrow, Clyde's brother, in Arthur Penn's tragicomic shoot-'em-up ''Bonnie and Clyde.'' It was here, says Mr. Hackman, that he learned to mine his own discomfort to fill out his characters. In an early scene in which a conversation with Clyde lapses awkwardly, he laughs and beats on his legs to fill the silence, and the gesture captures something essential about Buck: that he can't afford to stop and think too much. He's a friendly, not-too-bright guy who never connects with the horror he perpetrates; so when he's mortally wounded and he staggers around bleeding, clutching his gut and wailing, animal-like, it's the most painful death in a movie full of painful deaths.

His first leading-man role came three years later in the chamber drama ''I Never Sang for My Father'' (1970), and he had trouble with it. As the helpless son of a dominating father (Melvyn Douglas), he couldn't hide behind a cretinous accent or juggle a lot of props; he had to be emotionally naked, and he didn't especially want to open himself up to the grief of his non-relationship with his own dad. ''I didn't think a lot of the project and was taking it very lightly,'' Mr. Hackman recalls. ''Then Melvyn Douglas came up to me and said, 'Gene, you'll never get what you want with the way you're acting,' and he didn't mean acting -- he meant that I was not behaving myself. He taught me not to use my reservations as an excuse for not doing the work.''

The advice came in handy with his next big role, which Mr. Hackman nonetheless tried to back out of. ''Popeye'' Doyle was based on a real New York narcotics detective named Eddie Egan -- described by some as a big Irish blowhard who didn't think Mr. Hackman had anything like his own bullying force. In one of the first scenes of ''The French Connection'' (1971), Popeye had to slap around a drug suspect, but Mr. Hackman couldn't surrender to the sadism. He says he discovered the key to the character in a single gesture: Standing in a freezing parking lot eating a cruller, he calls out lewdly to a girl in boots, then he tosses the pastry over his shoulder and smirks. Suddenly he had access to Popeye's combination of flippancy and drive; he had permission to do anything. The upshot is the most physical of Mr. Hackman's performances, a sneering, finger-jabbing, cyclonic hero-monster.

The role -- and the Academy Award that followed -- made him a bona fide movie star, a tag with which he struggles to this day. He professes not to understand his appeal, hates watching himself on screen, and hasn't seen the majority of the more than 80 features in which he has appeared, most of them with his name above the title.''I can tell on the set if a scene works,'' he says. ''But for the life of me, I couldn't tell watching the finished performance.''

One performance he didn't need to see, and hasn't, was in the 1972 disaster picture ''The Poseidon Adventure.'' ''That was my idea of being a Hollywood movie actor,'' he says of the role, in which he was called upon, with a straight face, to direct the women to tear off the lower halves of their dresses for their own safety -- an edict that mysteriously didn't apply to the character played by Shelley Winters. ''When I was working on it, I was kind of ashamed of myself. I had to have my hair poufed up at the end and slicked over. And the producer, Irwin Allen, was one of those guys who used to comb his hair from one ear across the top of his head, and I just didn't want to look like him.'' Mr. Hackman seemed more at home that same year in the thriller ''Prime Cut'' as a barnyard gangster called Mary Ann. We first glimpse him sitting behind a plate of innards. ''You eat guts?'' asks the hero, Lee Marvin. ''Yeah,'' says Mr. Hackman brightly, smiling as he shovels a forkful of brown glop into his mouth. ''I like 'em.''