Her second marriage, in 1949, was more to Stalin’s liking. The groom, Yuri Zhdanov, was the son of Stalin’s right-hand man, Andrei Zhdanov. The couple had a daughter, Yekaterina, the next year. But they, too, divorced soon afterward.

Her world grew darker in her father’s last years. Nikita S. Khrushchev, Stalin’s successor as Soviet leader, wrote in his memoirs about the New Year’s party in 1952 when Stalin grabbed Svetlana by the hair and forced her to dance.

Defection

After Stalin died in 1953, his legacy was challenged, and the new leaders were eager to put his more egregious policies behind them. Svetlana lost many of her privileges. In the 1960s, when she fell in love with Brijesh Singh, an Indian Communist who was visiting Moscow, Soviet officials refused to let her marry him. After he became ill and died, they only reluctantly gave her permission, in early 1967, to take his ashes home to India.

Once in India, Ms. Alliluyeva, as she was known now, evaded Soviet agents in the K.G.B. and showed up at the United States Embassy in New Delhi seeking political asylum. The world watched in amazement as Stalin’s daughter, granted protection, became the most high-profile Soviet exile since the ballet virtuoso Rudolf Nureyev defected in 1961. The United States quickly dispatched a C.I.A. officer to help her travel through Italy to neutral Switzerland, but American officials worried that accepting her into the United States could damage its improving relations with Moscow. Finally, President Lyndon B. Johnson, on humanitarian grounds, agreed to admit her but asked that there be as little fanfare as possible.

Unknown to Washington at the time, the K.G.B. was discussing plans to assassinate Ms. Alliluyeva, according to former agency officials who were quoted by The Washington Times in 1992. But, they said, the K.G.B. backed off for fear an assassination would be traced back to it too easily.

Her arrival in New York, in April 1967, was more triumphant than low-key. Reporters and photographers were waiting at the airport, and she held a news conference in which she denounced the Soviet regime. Her autobiography, “Twenty Letters to a Friend,” was published later that year, bringing her more than $2.5 million. In 1969 she recounted her journey from the Soviet Union in a second memoir, “Only One Year.”