Yugoslav President Josip Broz Tito died yesterday after developing new heart trouble. He was 87 years old.

Tito died soon after his team of eight doctors issued a medical bulletin saying he had slipped into critical condition. He had been hospitalized for nearly four months following a blood vessel blockage that led to amputation of his left leg.

Tito's condition had temporarily stabilized last Wednesday, a week after he went into a coma and shock following a four-month battle with liver damage, kidney failure, high fever and pneumonia.

Harvard experts in Near Eastern affairs inverviewed shortly before Tito's death said they doubted it would prompt immediate Soviet intervention in Yugoslavia.

The greatest danger facing Yugoslavia, the experts agreed, is that the Soviets will either exploit the tensions among Yugoslavia's various republics, or encourage Bulgaria to provoke a border dispute with Yugoslavia and intervene in support of their ally.

Adam B. Ulam, professor of Government and an expert on Soviet foreign policy, said recently the Soviets will not exploit the tensions between Bulgaria and Yugoslavia unless specifically asked to do so by the Yugoslavian Communist Party.

"I don't think the Soviets will move either directly or indirectly against the Yugoslavs," Ulam said. The Soviets "will probably send a big delegation to the funeral to mourn," he added.

Richard Pipes, Baird Professor of History, said recently that while the Soviets probably will not stage a direct invasion of Yugoslavia, they will attempt to exploit dissent within the country.

"The Soviets will probably want to follow a policy of divide and conquer," Pipes said, adding that they will attempt to "dismember" the country rather than crush it directly.

Raymond T. Miller, an associate at the Russian Research Center, said last month that if the Soviets were interested in gaining control of Yugoslavia by invasion, they would have their satellite Bulgaria provoke a border dispute and then intervene. But he added that "this is not a real possibility."

David Stark, a graduate research fellow at the Center for European Studies, said recently the greatest danger facing Yugoslavia "is not a Soviet invasion, but rather that certain parties within Yugolavia will use the threat of such an invasion to move the country along more Soviet socialist lines."

Tito's death will not immediately affect the balance of power in the Near East, Stark said. "Yogolavia has been playing Russia off against the West brilliantly for 35 years, and that probably won't stop with Tito's death," he added.

Pipes disagreed, saying that Russia, Bulgaria and Hungary might "pounce on and pressure" Yugoslavia in an attempt to intensify hostilities among different political factions