The death of Constantin Chernenko and election of Mikhail Gorbachev stirred hopes throughout communist Eastern Europe that the curtain of uncertainty and paralysis that has enveloped the Kremlin in recent months will rise now on a new era of stable and predictable rule.

But just how that rule will translate into Soviet positions on economic reform, contacts with the West and freedom for Eastern European states to pursue specific national interests remains a cause for nervousness and conflicting desires, talks with Communist officials, academics and journalists in several Eastern Bloc capitals this month indicate.

Gorbachev's swift assumption of power today pleased advocates of reform who expect him to revive the spirit of dynamism that marked the brief tenure of Yuri Andropov as Soviet leader.

The new Kremlin chief is regarded above all by some Eastern Europeans who have met him as a strong proponent of economic modernization, flexibility and improved efficiency.

But a man who meets from time to time with senior officials in Hungary -- Eastern Europe's champion of economic reform -- said there is nonetheless some degree of anxiety here about how long it might take Gorbachev to consolidate his position and what compromises he may be compelled to strike along the way with more conservative elements of the Soviet leadership.

News of Chernenko's death was received without shock in this sophisticated communist capital. Although the Soviet leader's long illness had not been directly reported in the state-controlled press, in keeping with Communist practice to avoid such comments, it had been broadly hinted at, and many Hungarians as well as other Eastern Europeans, skilled at reading between the lines or tuning in regularly to western radio stations, were aware that Chernenko did not have long to live.

Moreover, the death of three Soviet leaders in less than three years has made the passing of a Kremlin chief a more commonplace and less cataclysmic occurrence than it once had been for Moscow's client states.

For the most part, the elderly Chernenko was viewed by Eastern Europeans as a transitional figure. Gorbachev's election at a relatively young age is seen as a sign other Soviet bosses are ready to accept him for what is likely to be a very long term, something they apparently were not prepared to do a year ago when Chernenko was elevated instead.

The announcement of the selection of a new Soviet party leader on the same day the death the former one was disclosed was an unprecedented congruence and created a dilemma for Communist editors trying to balance on tomorrow's front pages an appropriate show of grief for Chernenko and a cheering welcome to Gorbachev.

But one senior official here saw Gorbachev's rapid election as reflecting a mood of impatience and readiness for change in the Soviet Union that is already working in the new chief's favor.

Not everyone in the Soviet Union's satellite countries is hoping Gorbachev will shake things up in Moscow. In Czechoslovakia, the most conservative Warsaw Pact ally, which is still largely traumatized by the Soviet invasion of 1968 that choked an attempt at major reforms by now-discredited party leaders, officials are discomfited by the thought of new impulses emanating from Moscow.

"There is a trend to say we need young leaders, but the question is whether the leader of a country with lots of arms should be too dynamic," a Czechoslovak Foreign Ministry official remarked in a recent interview.

But a number of Hungarians have privately been saying that a dynamic, assertive Soviet leader would also serve the cause of East-West arms control. "The more self-confident, the better, because he would then be less afraid to bargain and reach agreement with the United States," a Hungarian party member said.

In the recent absence of a strong personality at the top in Moscow, Eastern European leaders with long and secure tenure have displayed greater authority in shaping their own foreign and economic policies.

Economic planners in Hungary and Poland have distanced their countries from the overly centralized Soviet model, adopting systems of less-direct controls on companies. In foreign relations, East Germany, Romania and Hungary have demonstrated more independence in dealing with the West.

Behind this growing show of national identity in Eastern Europe is a complex tangle of factors including public discontent with what socialism has yielded so far, real fears about leaving arms control and management of East-West contacts to the superpowers alone, and a mounting confidence and sense of security among such longtime rulers as Hungary's Janos Kadar, Romania's Nicolae Ceausescu and East Germany's Erich Honecker.

At the weakest point in the Soviet Bloc -- Poland -- an ever-restless population has forced the government of Gen. Wojciech Jaruzelski to open social vents by allowing the most liberal press in the Soviet Bloc and to seek allies among such traditional ideological adversaries as the Roman Catholic Church and private farmers, by offering them concessions.

Only the regime of Czechoslovak leader Gustav Husak continues unvaryingly to follow the Soviet line. Prague officials view the deviations among their neighbors with some concern, and look to the day a strong arm from Moscow will help draw differing socialist practices closer together again.

"I think that after a period of certain differentiation resulting from countries testing various management patterns, there will be a synthesis," said a Prague expert on international relations. "The positive aspects will be adopted by others and the negative ones will be given up by countries that invented them."

But other Eastern Europeans doubt their quest for self-assertion is reversible. They expect Gorbachev, as a pragmatist, to tolerate the widening variations among Warsaw Pact members rather than try to impose a new conformity on the communist alliance.