First he let a brilliant career slip into overblown, overpaid roles. Then his family slid into self-destruct. Where did Marlon Brando lose the plot, wonders David Shipman
As so often in the history of our modern Babylon, the headline seemed inevitable: "Brando's daughter killed herself". The tabloids put it on their front pages - hardly the place, one might have thought, for a sad little soul whose only claim to our attention is that she was who she was: Cheyenne Brando, the daughter of a very famous man.

As a young man, Marlon Brando was renowned for his acting. Conceivably he is better known now for the already half-forgotten California trial in which Cheyenne's half-brother Christian was sentenced to 10 years in jail for killing the young man whose child she was carrying. The sentence was in response to the plea-bargain negotiations of Robert Shapiro, currently appearing in another famous court case in Los Angeles, and one even more widely reported: the trial of OJ Simpson.

How many other women and children there have been in Marlon Brando's life is a secret, but his brother-in-law Dick Loving, who with his wife looked after Christian for a while at the order of a Santa Monica judge in 1965, said, "In certain ways he was kind of an incompetent father. The nature of his position and his own stresses made it very, very difficult for him to be a father. The life he went through, the number of women - there was no constancy there. I think that kid was totally deprived of stability."

As a young man, Brando himself observed, "You've got to have love. What other reason is there for living? It's been my trouble, my inability to love anyone." The grown-up Christian put it even more succinctly: "I was thinking, there's all that power to help, but Marlon didn't do shit."

He, Brando, is certainly regarded as the most widely known case of a film star selling out. Youngsters who have seen the ill-judged and self- indulgent performances of his later years find it hard to believe he was once a good actor, probably a great one. The difference in quality between his last half-dozen films and the early ones is indecent. He once, famously, said he could have been a contender. Instead, he is a joke, and the press, loving the contrast, has unhappily for him and his family kept him in the news.

This Saturday the BBC is showing On the Waterfront, made in 1954, for which Brando won his first Oscar - one of those occasions when the award was entirely justified. It was his sixth film in four years, during which time he revolutionised our concept of screen acting.

He played an embittered paraplegic in his first film, for Fred Zinnemann, The Men (1950), and it has one quality till then never found in an American movie hero, a je m'en fou-ism: he simply didn't care whether or not we liked him. As on Broadway, Elia Kazan directed him in A Streetcar Named Desire (1951), recapturing the animal magnetism of the uncouth, slobbish Stanley Kowalski, and again in Viva Zapata! (1952), in which Brando gave an eloquent account of the Mexican peasant leader.

Remembering On the Waterfront in his 1988 memoir, Kazan wrote, "If there is a better performance by a man in the history of film in America, I don't know what it is."

The decline was gentle at first, as Brando took on a series of contrasting roles: Bonaparte in Desire (1954), a singing Damon Runyon gambler in Mankiewicz's Guys and Dolls (1955), a Nippon translator in The Teahouse of the August Moon (1956), and the masochistic cowboy in One Eyed Jacks, which he directed himself after quarrelling with Stanley Kubrick.

He said in his own autobiography, "I am more surprised at how I turned out than I am about anything else. I don't ever remember trying to be successful. It just happened." But somewhere along the way something was mislaid: his talent.

That it had, after all, its limits was first demonstrated in the precious affectation of his Fletcher Christian in the second version of Mutiny on the Bounty (1962), the film out of which, in a sense, Cheyenne was born. Brando's satiric version of an aristocratic Englishman might have served for a five-minute sketch, but it palls over a period of three hours, much longer than necessary to tell this particular tale. MGM was so glad to have Brando that it gave him virtually unlimited control, not to mention $5,000 a day if shooting went over the schedule - which it did, not only due to Brando's demands but also due to his returning to face several court battles with his ex-wife, who was seeking to have him barred from seeing their son.

Cheyenne Brando, who hanged herself on Sunday, was conceived with Tarita Teriipaia, a Chinese-Polynesian dancer whom Brando had chosen for the only important female role in the film. Two years earlier he had married Movita Castenada, who had had the chief female role in the 1935 version; both the wedding and the subsequent divorce were carried out in comparative obscurity, but as much could not be said about his first marriage.

That, in October 1957, was to an Indian actress, Anna Kashfi - but it was over as soon as you could say Joan O'Callaghan - her real name, as her Welsh parents revealed the day after the wedding. She charged Brando with mental cruelty in filing suit in August 1959, after legally separating in September the previous year. A son, Christian, had been born in May, named after the actor Christian Marquand whose relationship with Brando "displayed an affection towards each other that far overreached the usual expressions of friendship". In her book Brando for Breakfast Kashfi claims that he was also courting the actresses France Nuyen and Rita Moreno.

Cameron Mitchell, acting with him in Desire, recalled Brando announcing "I'm trisexual". That became publicly known in 1983 when Brando told the French magazine Cine-Revue that he had "dabbled" in homosexuality: "For me sex is something you can't describe. If you like, let's say sex has no sex. Like the vast majority of men I've had several homosexual experiences and I'm not remotely ashamed of it."

The other consequence of the expedition to the South Seas was Brando's purchase of the island of Tetiaroa, where he communed with the sea and the sky, emerging to make a series of mainly indifferent films. Despite the much-publicised troubles on Mutiny on the Bounty, he managed to retain control over most of the films in which he consented to appear. There were those willing to pay Brando's huge fees for prestige purposes, for results as grotesque and overblown as his figure: Superman (1978), Apocalypse Now (1979), Christopher Columbus: The Discovery (1992). He was no longer to be savoured, but avoided. He felt similarly; Richard Donner, who directed Superman, reported: "I checked him out with various people and the one thing they all said was that Brando didn't like to work. If he could convince me to pay him and then release him he would."

John Malkovich, like most contemporary actors in thrall to Brando's early talent, once observed that Brando simply liked to enjoy himself; he liked jokes, larking around; and that he shouldn't be criticised for what he now did because he had achieved so much.

Brando's personal tragedies began in 1982 when his lawyer-agent, Norman Garey, who had presided over all his recent deals, shot himself; and when in 1983 Tetiaroa was struck by a hurricane, wiping out almost all his investment, he needed to work for those inflated sums. He was said to be selling the island, but in 1988 was reported to be living there with a Japanese lady, Yachio Tsubaki.

In 1989 Cheyenne was injured in a jeep crash on the island, and Brando blamed the accident for her subsequent bouts of depression. In May 1990 Christian Brando was accused of killing her lover, Dag Drollet, in an argument in Brando's Los Angeles villa. Christian claimed that the shooting was accidental, but that Drollet had been beating up Cheyenne - who fled to Tahiti when it was thought that "accessory" charges would be brought. She was questioned by the French authorities, who declared her "mentally incompetent". The son born prematurely was said to be "drug-addicted".

Cheyenne was said to have attempted suicide twice before the case came to trial, in February 1991, when the prosecution came up with earlier examples of Christian's violence. In 1986 young Brando assaulted his estranged wife, Mary McKenna Brando, and threatened to shoot her some months later during divorce proceedings. In 1989 it was alleged that he shot at an unemployed studio worker, Ricardo Alvarez, at almost point-blank range, but that Alvarez did not report this due to Brando's connections.

At the trial the senior Brando tried to take some of the blame for what happened. His private life might be summed up by a remark the dead girl once made, "He uses women, he used my mother". The final, haunting, professional comment might be that of Joanne Woodward, who co-starred with him in The Fugitive Kind: "I hated working with Marlon Brando - because he was not there, he was somewhere else. There was nothing to reach on to."