If Mikhail Gorbachev's recent meeting with the American president was important for his future and that of his country, the way he handles the president of Russia may be even more critical. Gorbachev and Bush proved once and for all that the East-West Cold War is over. Now it will be up to Gorbachev to demonstrate to his increasingly restless and dissatisfied countrymen that he can apply the same diplomatic skills that he used to win over the West to accommodate his new rival, Boris Yeltsin.

This is, if ever, the moment to implement "new thinking" on the explosive domestic front. Both Gorbachev and Yeltsin must recognize that their futures are intertwined, and that the success of one may be crucial for the other. Conversely, the failure of one may result in mutually assured destruction.

Yeltsin, the most radical of the reform-minded politicians to enjoy massive public support, was formerly a Gorbachev prote'ge'. Brought to Moscow in the early days of perestroika, the flamboyant and driven party chief of Moscow remained a dedicated advocate of radical change even after he was expelled from the Politburo for pressing too hard to increase the pace of reform. It was the circumstances of his departure, however, that proved to be humiliating and made him deeply bitter. Gorbachev, for his part, felt let down by his subordinate's outspoken prodding, and in the end offended and betrayed.

With the Soviet Union at a crossroads economically and politically, can these men put style and personality aside and form what would seem like a natural alliance?

On the face of it, there is no reason why it is not possible for the two to work together. Their platforms have many similarities: both believe in arms reduction, defense reform, movement to a market economy and the establishment of a state based on law. Furthermore, in a coalition with Yeltsin, Gorbachev could draw on Yeltsin's popularity, thereby engaging a base of support that could be critical during the hard times ahead. Alone, the never-popularly-elected Gorbachev might not be able to withstand public reaction to the painful process of moving toward a market economy.

Yeltsin also offers Gorbachev a formula that might save the union of republics, however loosely linked. Yeltsin's Russia and its recent declaration of sovereignty are bound to bring the issue of autonomy into the mainstream of political thinking. If Gorbachev recognizes the opportunity, he might use this development to take a new and urgent look at how to work out a new relationship with all of the republics.

Russia, as the most powerful of the republics, with more than 50 percent of the population and almost 90 percent of the natural resources, is too big to relegate to isolation (as was the fate of Lithuania). With Russia now joining the movement for autonomy from Moscow's central rule, Lithuania and the Baltics can no longer be viewed as on the political fringe. In other words, now that the Russian horse is barging its way out of the stable, chasing the big one and enticing it back might also work for the others that have already bolted. In this respect, Russia's new stance could be a blessing in disguise.

Despite the obvious bonuses that joint efforts could produce, it might be easier for Mikhail Gorbachev to reach a cooperative working relationship with George Bush than with Boris Yeltsin. Finding common ground with Yeltsin and his supporters would mean he would have to overlook some fundamental differences in their approach to perestroika.

One of the most important issues during Yeltsin's campaign for the presidency, for instance, centered around his view of socialism. Yeltsin was heavily criticized for failing to mention, let alone promote, "socialism" in his electoral speeches. Gorbachev, himself a professed Communist and a "convinced socialist," complained that Yeltsin did not use the word socialism "even once" in his campaign speech for the Russian presidency. ". . . {W}ith one stroke of the pen," Gorbachev said," "{Yeltsin} invites us to part with the socialist choice of 1917."

Two days later Yeltsin reacted to the attack when he told the Congress that there have been forms of socialism, such as "developed socialism" (referring to Brezhnev-style socialism), "national socialism" (a la Hitler), and "Pol Pot socialism" (as in Khmer Rouge). Yeltsin concluded, "I do not believe in socialism for its own sake. I believe that the people of this country should live well, that the people should respect the leadership and the supreme authorities of their country, of their republic, and that vice versa, the supreme authorities of the republic should respect their people."

As rhetorical as it might sound, this dispute already has had practical implications of overwhelming importance. The issue of one's dedication to socialism is not an academic point, especially with the Communist Party on the brink of a searing split.

In addition to basic definitional questions about the Communist Party, the concept of socialism is also relevant to the debate about the scope and pace of economic reform. At the heart of economic transition is the issue of private property. Here both men are in conflict. Although Gorbachev has said he supports private property, the bill that went through the Supreme Soviet recently dealt with most forms of private property except ownership of land; here it simply called for leasing. Yeltsin, on the other hand, said the week before last that "it is essential to embark on the sale of non-traditional goods to the republic's population: plots of land, unused equipment, machinery and material from state enterprises, and mothballed installations, and shares in the property of state enterprises. . . . "

Later, when Yeltsin responded to charges that he is nothing more than a populist who takes his positions based on what will sell, he said, "Populism? I don't consider this an abusive word. In my opinion, the greater part of this word consists of links with people."

Such statements remind us that Yeltsin, although still a member of the Communist Party, has become increasingly disenchanted with the party elite and its monopoly on power. Despite the repeal of Article 6 of the Constitution guaranteeing the party's leading role in society, Yeltsin feels that in practice, the party's position is essentially unchanged. Gorbachev, trying to avoid a split in the Communist Party, hesitates to take on such issues. But Yeltsin, interested in seeing the growth of his form of perestroika, sees no alternative to attacking the entrenched Communist Party apparatus. Such differences in ideological orientation at this juncture -- less than three weeks away from the decisive Communist Party Congress -- put the two men at significant odds.

But the very existence of such differences -- especially aired openly -- should only instill confidence about the pluralistic future that both men say they support. Only "new thinking" on the domestic front can avoid a deepening deterioration of morale and determination among the Soviet people. The last pressure the fragile social balance can withstand at the moment is a Cold War between the country's two most powerful and visible competitors -- particularly because they are vying for the same constituents sympathetic to reform. Coexistence must find its place in Soviet centrist and left-wing domestic politics. If it doesn't, protracted conflicts at the most visible levels will arrest the progress of perestroika and the development of pluralism. In that scenario there are no winners. But the losers? Most certainly: the Soviet people. Susan Eisenhower is a consultant to Western companies on the political and economic situation in the U.S.S.R. Roald Sagdeev, former director of the U.S.S.R.'s Space Research Institute, is a member of the Congress of People's Deputies.