Joseph Stalin's daughter, Svetlana Alliluyeva, and her 14-year-old daughter have been given permission to leave the Soviet Union, although their dates of departure are not set.

Alliluyeva said today that she would leave sometime after her daughter, Olga Peters, who she expects will be going back to England in the next week to attend boarding school there. Alliluyeva would not say where she herself would go, or when she plans to leave except that it would be "before the end of the month."

The two came to Moscow from the Soviet republic of Georgia on March 27 and have been staying in the Sovietskaya Hotel awaiting permission to leave the country. Both have U.S. as well as Soviet passports.

Peters applied for and received a British visa, which is required for persons traveling on Soviet passports. So far, her mother has not applied for one.

Alliluyeva, whose defection to the West in 1967 embarrassed the Soviet Union, returned here with her daughter in October 1984. Her arrival was publicly greeted by the Soviet press, and the restoration of her Soviet citizenship was announced on national television.

At the time, her return was seen as a signal to Soviets abroad that they could return and live here quietly and respectably. At a news conference shortly after her arrival, Alliluyeva said she had not enjoyed "one single day" of freedom during her years in the West.

The two moved to Tbilisi, capital of Georgia, a mountainous republic in the Caucasus, where they were warmly received, according to Soviet reports.

Stalin, whose brutal methods left permanent scars on Soviet society, is still revered by many in Georgia as a national hero.

Peters, whose American father is an architect, said in a telephone interview today that she was "thrilled" to be going back to school in England, but hoped to be able to return to Georgia for a visit someday.

"I myself became pretty attached to Georgia," she said. "I really love the place."

Peters said she now speaks Georgian better than Russian, which she apparently barely knew when she arrived 18 months ago. She said she had brought a dog with her from Georgia and that it was living with her at the hotel.

The Sovietskaya, one of Moscow's few elegant hotels, is used to house official guests. Alliyueva and her daughter stayed there when they arrived secretly from London in 1984.

Peters said she did not know when she was leaving for England, only that she was supposed to start school on April 16.

She said she did not know her mother's plans. "All she has told me is that she is sorry she came back," she said.

Viktor Louis, a well-connected Soviet journalist who sometimes serves as a conduit for official information, said today it was his understanding that Alliluyeva has been given permission to leave, but he said that she may first be going to Tbilisi to gather up her things.