The only advance publicity for Strawhead was a paragraph in the New York Times, but if you’re Norman Mailer you generate your own. By the end of its two-week run the play had become a celebrity event. Seated on folding chairs in the legendary Actors Studio on West Forty-fourth Street, a select audience that included—all on the same night!—Dustin Hoffman, Al Pacino, Robert De Niro, and Elia Kazan witnessed Mailer’s latest rumination on the former wife of Arthur Miller.

Onstage, decked out in a tight pink sweater, a platinum wig, and a lot of eye makeup, young Kate Mailer, a twenty-three-year-old Brown University graduate who had acted in college and had a minor part in an amateur repertory production of Hair, amazingly became Marilyn. She whimpered and flirted, was seductive and coy; she babbled to herself in a nervous, breathy voice; she emanated sex. “Libido seemed to ooze through her, and ooze out of her like a dew through the cracks in a vase,’’ Mailer wrote in Marilyn, his 1973 coffee-table biography. Never mind the prose. What he meant to say was that Monroe was sexy—and so was Kate in her father’s dramatic version of some ancient evenings.

Kate is the sole offspring of Mailer’s brief marriage to Lady Jeanne Campbell, daughter of the Duke of Argyll and granddaughter of Lord Beaverbrook. Mailer’s current wife, Norris Church, also had a major part in the play, and his son Stephen was the stage manager. “When you have this big a family,’’ Mailer reasoned, “you might as well put them to work.” But wasn’t it a little. . .odd to cast one’s own daughter in a role that required her to bed down with a decadent goon and simulate sex on a motorcycle? “I try to have the detachment of the artist,” Mailer stressed, “and Kate had a natural affinity for the role.”

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Around his daughter, Mailer was scarcely recognizable as the swaggering bully who dominated the PEN Congress in New York the same week Strawhead played. His manner was gently, touchingly paternal. “She was the best prep-school actress I’d ever seen,” he recalled of her performance as Joan of Arc in Jean Anouilh’s The Lark when she was a senior at St. George’s School. “Dad said, ‘Forget about college. Just come to New York and act,’ ” Kate remembered. “But I didn’t feel I was ready yet.” There was nothing disingenuous about her modesty, and it was hard to believe that the shy girl bantering with “Dad” backstage was the slatternly sex bomb from the play. Milky-skinned and auburn-haired, she could have been a coed home from college for the holidays. “Did you get a haircut?” she asked her father. “You look so cute.”

The play was a family affair, but the playwright was utterly in earnest. Sitting intently in the audience night after night with a few of his numerous progeny by his side, Mailer could have been a high-school drama teacher directing his twentieth Taming of the Shrew. Pencil in hand, he made notes on a yellow pad, leaned forward, grinned at a good line. Strawhead had been kicking around for years, and he was determined to make it work. Begun as a possible Broadway play adapted from Mailer’s second Marilyn book, Of Women and Their Elegance, it gradually metamorphosed into a more experimental work. Now it’s a candidate for Off Broadway. “If the play doesn’t go this time, it’s not going to go,” says Mailer. “I can’t afford to write for the theater.”

The opening night was pretty ragged, a “read-through” so bewildering that when a woman in the audience disrupted the play those who hadn’t noticed the “Espontaneo” listed in the program thought she was for real. There was a lot of play-within-a-play business: the “director” and “producer” yelling, the “playwright” yelling, Kate protesting, “How do you know Marilyn did things like this?” There was a bad moment when the actor playing the director asked how many wanted the play to go on, and was answered with silence. (“A poor idea,” Mailer conceded afterward.)

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It was Kate who really made the show. For three hours, with never a moment offstage, she rehearsed Marilyn’s doomed marriages and disastrous affairs, her cinematic triumphs and private failures of nerve. Her evocation of impending tragedy was magnificent. Seated at her vanity table, she brooded and whined, vacillating between a wistful elegiac voice (“I’m so rosy I want to dance”) and a brutal estimate of her vulnerability: “It’s the fellows with the nicest faces who always drill that tiny little hole in your heart.” This is late Marilyn, the Marilyn addicted to pills and champagne, the world-famous icon on the downslide to an early death.

Strawhead is a “memory play,” Mailer explained—memories that happened, and memories that never did. Biography isn’t Mailer’s intention. His research, he confessed in Marilyn, would “stray toward the borders of magic”—that is, pure invention. Reverting to his weird cabalistic ways, he dwelled on the anagrammatic significance of the fact that the letters in Marilyn’s name, “(if the ‘a’ were used twice and the ‘o’ but once),” would spell his own name, “leaving only the ‘y’ for excess.” The play is less mystical, more grounded in actual events; but it has its own share of poetic license. “I’m trying to comprehend Marilyn,” says Mailer’s imaginary playwright, “and I think we have to assume there were buried horrors in her life. Something kinky.”

Are these assumptions justified? It hardly matters. Strawhead is less about Marilyn than about Mailer’s quest for Marilyn. And what better way to approach this mysterious shiksa than through Arthur Miller, another guy from the wrong side of the Brooklyn Bridge who happened to become a famous writer. Mailer’s portrait of Miller in Marilyn is both pitiless and sympathetic. Puritanical, parsimonious (“find the witness to testify that Miller had ever picked up a check”), a ‘‘tall and timid hero of middle-class life, as guarded in his synapses as a banker,” the playwright is in every way the volatile novelist’s opposite. “He was sufficiently pontifical to become the first Jewish Pope, he puffed upon his pipe as if it were the bowl of the Beyond, and regaled sophisticated New York dinner parties with tedious accounts of his gardening and his well-digging, he was a Hamsun and Rolvaag of the soil, a great man!”

Kate: “Dad said, ‘Forget about college. Just come to New York and act. ”

Mailer: “She was the best prep-school actress I’d ever seen.”

In Strawhead Miller is again the complacent country squire, boring people with his accounts of clearing fields, gardening, the joys of plumbing. (“Nothing like taking a bath in water that comes through pipes you threaded yourself.”) Worse, Miller is a prude. The night they met, Marilyn recalls, “we didn’t do a thing. We just sat in a garden and talked. He held my big toe.” A nerd in white socks who doesn’t know how to cope with America’s blonde sex goddess. Who could? Well, if you dropped an “l” from Miller’s name and substituted an “a”...