The Reagan administration's offer of sanctuary to deposed Philippine president Ferdinand Marcos -- coming just a week after another former president, Jean-Claude Duvalier of Haiti, was turned down for haven -- has again raised questions about when the United States should offer political asylum to dictators it once backed.

Finding refuge for such people is often the price that U.S. policy makers must pay to get them to relinquish power. But allowing the former rulers into the United States poses thorny political and diplomatic problems -- particularly if a country's leaders seek to put the former head of state and his cronies on trial and request their extradition.

Also considered is the nature of the former rulers' alleged crimes. Drawing a line between Marcos and Duvalier, Rep. Jim Leach (R-Iowa) said yesterday that "the appropriateness of sanctuary rests primarily on a fundamental distinction between a mass murderer and a mass burglar."

The late Nicaraguan dictator Anastasio Somoza was given refuge in Miami in 1979 under an arrangement to persuade him to abdicate. But his presence posed a dilemma for President Jimmy Carter, who was trying to gain influence with the Sandinista government, which replaced Somoza. Nicaragua requested his extradition, but Somoza let Carter off the diplomatic hook by going to Paraguay, where he was assassinated in 1980.

Carter also invited Mohammad Reza Pahlavi, shah of Iran, to come to the United States in 1979 when his hold on power became untenable and Carter was interested in seeing a moderate democratic force take over in Tehran. But the shah chose to go to Morocco, with the hope that the revolution in his country would falter and he would be invited back to the Peacock Throne.

He was not invited back, and his invitation to the United States was rescinded by a Carter administration then fearful that giving him exile might spark anti-American attacks in Iran.

The shah was allowed to come here in October 1979 for medical treatment, an action that sparked the taking of 56 hostages at the U.S. Embassy in Tehran by radicals demanding he be returned for trial.

Philippine President Corazon Aquino vowed early in her campaign that if she unseated Marcos she would put him on trial for the 1983 murder of her husband, opposition leader Benigno Aquino Jr. The vow caused alarm among Aquino's supporters, who said such statements would harden Marcos' resolve to stay and bolster his support among military officers who might be implicated in the killing.

Lately, Aquino has called for "reconciliation."

The pattern for countries moving from dictatorship to democracy seems to be that the ex-leaders are rarely brought to trial. Of 10 Latin American countries that have made the transition since 1978, only Argentina tried former junta members for human-rights abuses.