Standing in the white hall of the Livadia Palace, the Soviet tour guide affects a touch of reverence as she points to a nondescript round table. "It was at this table . . ." -- she pauses for effect -- "that the victors over Nazi Germany decided the postwar structure of Europe."

Then she invites the group of middle-aged Soviet tourists to examine a painting on the wall depicting the scene in this same room on Feb. 11, 1945, the day the Yalta agreements were signed. The leaders of the three wartime allies -- the United States, the Soviet Union and Britain -- are seated around the table with their advisers. Already gravely ill, Franklin D. Roosevelt is huddled up close to the fireplace. Winston Churchill looks somewhat grumpy.

It is only Joseph Stalin, the shoemaker's son turned unchallenged ruler of the Soviet empire, who seems completely at ease.

The Livadia Palace in Yalta is a fitting place to begin an investigation of Russia's East European fiefdom as it enters a new era, the era of Yuri Andropov. Yalta has become a kind of historical shorthand for the division of Europe between East and West. For some, the word has come to mean the shameful betrayal by the Western allies of 100 million inhabitants of Eastern Europe. For others, it is the source of four decades of peace in Europe -- the longest period of stability that the continent has known for centuries.

A former summer home of the czars overlooking the Black Sea, the Renaissance-style Livadia Palace has been lovingly restored as a tourist attraction by the present Communist government. Tens of thousands of Soviet vacationers are shepherded through its marble-lined corridors every year by guides who seem to know their script by heart. The political message they drum into the heads of the tourists is that it was here, in the Crimea, that Soviet Russia achieved its rightful recognition as a superpower following its enormous sacrifices in World War II.

A related message is that the results of that war must never be tampered with. To do so, in the view of the Kremlin's leaders, is to risk a new and potentially even more disastrous conflict.

History shows, however, that no man-made order is ever permanent. Empires rise and fall. A generation has passed since the end of the war and -- with the exception of Andrei Gromyko, the veteran Soviet foreign minister -- all the men who helped negotiate the Yalta accords are long since dead or retired from active politics. It is scarcely surprising, therefore, that the political status quo associated with Yalta should today appear shaky, even if it still remains in place.

During the past few years, the Soviet Bloc has been beset by growing economic, political and ideological strains. The crisis is most advanced in Poland where, a year ago, a Communist government had to be rescued by its own Army in order to remain in power. But the symptoms of decay are visible throughout the region -- from widespread political apathy to ill-lit streets and empty shops to massive and growing corruption.

The thesis that the Soviet Empire is, in the long run, doomed has been developed by President Reagan. In a speech to the British Parliament in June, he predicted that "the march of freedom and democracy . . . will leave Marxism-Leninism on the ashheap of history as it has left other tyrannies which stifle the freedom and muzzle the self-expression of the people."

More surprisingly, Enrico Berlinguer, the leader of the Italian Communist Party, has publicly doubted "the capacity for development and renewal" of the Communist societies of Eastern Europe.

A tour of Eastern Europe provides plenty of evidence to support one element of what could be called the "Reagan-Berlinguer line": that the Soviet Empire is undergoing a crisis of faith more profound than anything the West is currently experiencing. Conversations with Communist Party officials, dissidents, diplomats, historians and ordinary citizens reveal, however, a divergence of opinion about whether the decline is inexorable or whether, given dynamic new leadership, it can be halted or even reversed.

The crisis of faith--the crumbling of the belief that communism can provide the masses with a rich and abundant life, let alone overtake capitalism -- assumes different forms in different countries.

In Poland, statues of Vladimir Ilyich Lenin, the founder of the Soviet state, have been set on fire by enraged workers chanting slogans like "Long live Reagan" and "Junta, back to Moscow."

In Czechoslovakia, now "normalized" after the crushing by Soviet tanks of "socialism with a human face" in 1968, the odd political slogan still appears on a stretch of whitewashed wall, known as "Democracy Wall," in Prague's Old Town. But most people have withdrawn into themselves.

In Hungary, the first Soviet Bloc country to introduce serious economic reforms, energies are devoted to getting rich quick.

In the Soviet Union, one of the best illustrations of the ideological malaise is the revival of interest in Stalin. The latest Stalin cult has sprung up from below and is the product of a centuries-old yearning for a strong ruler who will make Mother Russia respected abroad and maintain order and discipline at home.

In the guest book at the Livadia Palace, some visitors have complained about the lack of official recognition for Stalin's achievements. One typical comment, from a "war veteran," read: "I find it a great pity that there's no separate portrait of Stalin here. He was as much a part of our history as Churchill is of England's."

Later, over dinner, a young Russian actress who certainly was born after Stalin's death in 1953 told a Western visitor why she thought the late dictator was "a great man."

"Our lives at the moment have no direction," she said. "Ten percent of the people work while the others cheat. We need someone like Stalin to get this country into shape again."

It is difficult to believe that the actress, whose main interests appeared to be Western fashions and Western music, would really have welcomed a return to the days of the great purges and the gulags. But her feelings about Stalin, which were evidently absorbed from her parents, reflect the unease of many Russians with the drift and stagnation that accumulated during the 18-year rule of Leonid Brezhnev.

It is significant that at Brezhnev's burial in Red Square last month, there was none of the wild grief that accompanied Stalin's funeral. Stalin was seen by Russians as the autocratic ruler of a vast empire, the spiritual heir of men like Ivan the Terrible and Peter the Great. Brezhnev, by contrast, was perceived more in the role of a powerful bureaucrat administering the emperor's legacy.

This psychological difference is also felt by the people of Eastern Europe. When Stalin died, there was widespread anticipation of sweeping changes -- a mood that resulted in the subsequent upheavals in East Germany, Poland and Hungary between 1954 and 1956. Now, however, there is little expectation of major change coming from above: for all its failures, the system has become much more entrenched.

The French political commentator, Andre Fontaine, has described the Soviet Bloc as "an empire without an emperor." In an article in Le Monde on Brezhnev's death, he wrote that none of Stalin's successors had filled his role of charismatic leader capable of exciting and channeling patriotic devotion. He depicted the Kremlin as militarily strong but ideologically enfeebled -- the headquarters of a worldwide religion with scarcely any true believers left.

The decline in the ideological appeal of communism has, however, made little difference in the way Soviet leaders look at Eastern Europe. Transcripts of the Yalta Conference show that Stalin was brutally frank with Roosevelt and Churchill. He couched his arguments in terms of realpolitik and Soviet national interest: After years of war, Russia had earned the right to secure borders. And security, in Stalin's view, meant the installation of "friendly" governments in Eastern Europe.

The Soviet interpretation of what was agreed at Yalta has been disputed by Western historians. They point out that the Yalta agreements committed Moscow to allowing "free and fair" elections in Poland -- a promise that was never kept. In addition, there is no explicit mention of the division of Europe into spheres of influence.

The fact remains, however, that the Western allies did in practice recognize an overriding Soviet interest in Eastern Europe at Yalta. This was not because Roosevelt and Churchill somehow were outwitted by Stalin. It was simply the result of the military situation at the time. When the "Big Three" met in the hastily refurbished Livadia Palace, with the devastation of war still visible around them, the Red Army already had battled its way across Poland and was preparing for a final assault on Berlin.

Stalin's position was similar to that of the Russian czar, Alexander I, at the Congress of Vienna in 1815 following his victory over Napoleon. "The emperor," noted the British foreign secretary of the time, "insinuated that the question of Poland could end only in one way, as he was in possession."

The territorial results of World War II were summed up by the former Yugoslav ambassador to Moscow, Veljko Micunovic, who noted in his diary that Western powers such as Britain had lost most of their colonial possessions.

In some wonderment, he added: "Only the U.S.S.R. increased its national territory, both in the West and in the East. So this state, which was already the biggest in the world, became even bigger -- and its small neighbors became even smaller. And I am not even speaking of the fact that the U.S.S.R. included in its orbit another seven European socialist states."

All Soviet leaders since Stalin have done everything possible to protect this inheritance. Safeguarding "the gains of socialism" was the argument used by Nikita Khrushchev for invading Hungary in 1956. The same logic was used to justify the Soviet intervention in Czechoslovakia in 1968 and the military crackdown in Poland. It is a deeply ingrained Russian view that territory won must never be given up -- or the whole empire could start to crumble.

During the Solidarity days in Poland between August 1980 and December 1981, there was talk in the West of the possible "Finlandization" of Eastern Europe. Western pundits argued that decades of Communist domination had turned the region into a chronic source of political and economic instability. Finland, by contrast, seemed to provide a model for a prosperous, Western-style democracy that scrupulously respects the foreign policy interests of its large Soviet neighbor. Might not the Soviets agree to the same formula being applied in countries such as Poland rather than face the trauma of recurrent crises?

Hopes of "Finlandization" collapsed abruptly following the military crackdown in Poland. In fact, they were always based on a false comparison. The way the Kremlin looks at Finland, a country of less than 5 million people on the political periphery of Europe, is quite different from the way it views Poland, a country of 36 million that straddles its main communications lines with the 20 Soviet divisions stationed in East Germany.

An independent Polish economist, Rafal Krawczyk, noted in a private memorandum circulated in Warsaw recently that the Kremlin was very sensitive to any questioning by the West of Soviet rights in Poland. Poland, he said, is "the key to Soviet policy toward Germany" and "the foundation of the Yalta system."

"The Russians have learned one basic lesson about Poland from their history. The periods when Poland has been out of Moscow's sphere of influence have coincided with the loss by Russia of its dominant influence in Europe," he wrote.

Poland certainly has a special significance in Russian history and culture. Stalin labeled it "that corridor through which the Germans march into Russia," and Soviet propagandists never tire of pointing out that 600,000 Russian soldiers died on Polish soil in World War II. The two nations are historical enemies: At the monastery of Zagorsk near Moscow, Russian Orthodox priests still regale visitors with stories of the atrocities committed by Polish troops there in the 17th century.

A memorial tablet reads: "Three plagues -- typhus, Tartars, Poles."

In the Bolshoi Theater's production of the opera "Boris Godunov," there is a striking change of atmosphere as the scene shifts from the lavish palace of the autocratic Russian czars to the refined Polish court with its stained glass windows and elegant manners. Poland is depicted as a place where Roman Catholic prelates wield a sinister influence behind the throne.

"That's how Russians see Poland -- and, for that matter, Eastern Europe too. It represents a different culture of which they are part envious, part contemptuous and part afraid. The region is both their gateway to the West and their protective barrier from Germany and fears of U.S. encirclement," a Western diplomat in Moscow commented.

Despite the latest events in Poland, many East Europeans acknowledge that there has been some loosening in the Soviet stranglehold. As evidence, they point to the length of each successive revolt. The Hungarian uprising in 1956 lasted just a few days before it was crushed. The "Prague Spring" in Czechoslovakia blossomed for seven months in 1968. The Solidarity era in Poland lasted for 16 months -- and its effects are still reverberating around the bloc.

Romuald Kukolowicz, 60, a sociologist who acted as an adviser to Solidarity, believes that it is possible to trace a steady evolution in Soviet attitudes to Eastern Europe. He first encountered Soviet soldiers in 1939, when, as a result of the pact between Stalin and Hitler, they overran his hometown of Vilnius, which later was incorporated into the Soviet Union. Like many other Poles, he was forced to migrate to the western part of Poland at the end of the war.

"While Stalin was alive, everything in Poland had to be a copy of the Soviet Union. After Khrushchev took over, we got more room for maneuver. And however we assess Brezhnev, he certainly showed more concern for consumption than his predecessors," he said.

Kukolowicz believes that successful revolutions can be divided into four phases. The first generation (Lenin) comprises the creators of the revolution and the second (Stalin) its consolidators. The third generation (Khrushchev and Brezhnev) seeks simply to maintain and continue what already has been achieved, while the fourth presides over its erosion.

"Right now, we're somewhere between the third and the fourth stage," Kukolowicz said.

Brezhnev's death marks the end of an era for Eastern Europe as much as for the Soviet Union. Throughout the region, a new generation of politicians is coming to power. The changeover already has taken place in Yugoslavia with the death of Marshal Tito and Poland with the removal of Edward Gierek.

Hungary's Janos Kadar is 70, Bulgaria's Todor Zhivkov 71, East Germany's Erich Honecker 70, Czechoslovakia's Gustav Husak 69, and Albania's Enver Hoxha 74. Nicolae Ceausescu of Romania, physically the most vigorous of East European leaders, is 64.

During the past decade, Brezhnev made a tradition of inviting other Soviet Bloc leaders to join him on his summer holiday in the Crimea. One by one, they would have their pictures taken with Brezhnev at his dacha just a mile down the road from the Livadia Palace. It was a kind of symbolic annual outing for the political heirs of the Yalta agreement.

As the years went by, the faces in the holiday snapshots became visibly more decrepit and the words in their communiques steadily more empty. Last summer the ritual was broken when three of the leaders failed to show up. It was a sign of the times. Within three months, the caretaker of the Soviet empire was dead, leaving a legacy to his successors of huge territories, massive military might and a host of unresolved problems.