In many ways, the woman who called herself Lana Peters resembled millions of Americans.

Like many in this land of immigrants, she had come from another country to seek a happiness here she could not find at home. She spoke English with a foreign accent, as many here do.

Like millions of us, she moved restlessly from place to place, seeking the ideal location, where friends and congenial surroundings would be just right. Her addresses spanned the continent: Princeton, N.J.; Scottsdale, Ariz.; Oceanside, Calif.

Like almost one marriage in three here, Lana Peters' marriage failed, and for many years she lived the exhaustingly lonely existence of the single parent.

She doted on her daughter, Olga, and vowed never to teach her the language of Mother Russia.

This vow told the secret of Lana Peters' identity. For this 58-year-old woman with light, curly hair, broad face and wide clear eyes, whose lifestyle and biography seemed so very American is Svetlana Alliluyeva, daughter of Joseph Stalin, dictator of the Soviet Union from 1929 to 1953. She caused a sensation by defecting to the United States in 1967, and recently returned to her homeland.

In the opinion of friends and acquaintances who knew her during the 15 years she lived in the United States, it was the burden of being Svetlana Stalin that disrupted her life and shattered her quest for security and happiness. They described a woman capable of intense emotional relationships, but prey to deep suspicions and nameless fears that bordered, according to several persons, on paranoia.

"As I grew up, I became rather afraid of my father," she told an interviewer several years ago.

Friends and acquaintances said she could break friendships abruptly and completely and struggled with a fierce temper. Although she reached out for contact, she also was said to be withdrawn and remote, a person who could spend an entire evening with friends but speak hardly a word to anyone.

"She was very, very lonely and concerned about her situation," said her former husband, William Wesley Peters, who is Olga's father. Peters, an architect, was married to Alliluyeva from 1970 to 1972.

"I feel very sorry and concerned for her," he said. Peters, 72, said he last talked to Alliluyeva in August, when he called her in England, where she had moved in August 1982 after several years in Princeton. He said she gave no hint she might have been considering returning to Russia, from which she defected 17 years ago.

She had settled in the New Jersey university town to be near such noted Soviet scholars as Geroge F. Kennan, Cyril Black and Robert Tucker. But over the years, her relations with many of these specialists cooled.

Peters said he last saw his daughter in the summer of 1983, when Alliluyeva sent Olga to summer camp in Wisconsin.

"I have no facts, not the slightest knowledge beyond what the media has reported," Peters said. His daughter, born May 21, 1971, in California, is a U.S. citizen.

Alliluyeva became an American citizen some years ago. In 1979, in a rare interview, she said, "I can't wait to vote" in a U.S. election. "Citizenship changed the whole quality of my life."

She achieved one capitalist dream when royalties from two books, "Twenty Letters to a Friend" and "Only One Year," brought her more than $1 million. But financial troubles and bad investments had eaten up most of the fortune. She lived modestly here and in England.

And in recent years, her enthusiasm for the United States flagged. Last March, in an interview in England, she declared that "no two nations are so similar as the U.S. and Russia."

She was feeling the relentless tug of her homeland and the life she had abandoned there, which included two grown children, Joseph Morozov and Yekaterina Zhdanova, by her first and second marriages.

"I do not believe in regretting one's fate," she said, "but sometimes it is very hard. I have not seen my son and daughter in 17 years, and have never seen my grandson and granddaughter.

"Sometimes," she continued, "it's an almost superhuman effort not to drop everything and run and get a ticket to go and see them."

In the end, that is what she did.