PRESIDENT Bush's summit schedule in Moscow and Kiev represents an attempt to avoid taking sides in the high-powered tug of war between the Soviet central government and the independence-seeking republics.For the first time at a superpower summit, the domestic Soviet scene is a central concern of both sides. As a top White House aide involved in organizing the summit puts it: "One of the things we need to be acutely aware of is that we don't want to become part of the problem." The formal business of this summit is the signing of the first-ever treaty that reduces the number of strategic nuclear weapons on both sides. In that sense, this is the last summit of an era that began with the Nixon-Brezhnev summit in Moscow 19 years ago. Since then, US-Soviet relations have pivoted around arms control - a continuous, competitive negotiation for stable equilibrium between cataclysmic weapons. But White House officials stress that this is not really an arms-control summit. Instead it is an attempt to shape a new, evolving relationship based on trade and cooperative - not competitive - security arrangements. Bush brings four major topics of discussion: The internal politics of the Soviet Union, especially the relationship between the Soviet center and the republics, complicate relations for the US. The Bush administration supports democracy and self-determination but also stability. Bush seeks a stable relationship while not taking sides. The US seeks further free-market reforms in the Soviet economy. This is likely to take the form of improved trade relations, not subsidies sought by the Soviets, such as a fund to back the international convertibility of the ruble. Bush hopes to expand on the cooperation forged between the US and Soviets in the Gulf war and apply it to other world hot spots. The Soviet Union is a supporter of the current Middle East peace process, although the Americans are clearly leading it. "I think we are trying to allow the Soviets a sense of participation in the Middle East," says William Cromwell, a professor of international affairs at American University. The leaders will discuss where to go next in arms control. The expert consensus in both Washington and Moscow is that arms-cut talks will pause now as the current agreements settle into effect. Bush will talk about the American fail-safe system for preventing accidental nuclear launches and about how to stem the proliferation of nuclear weapons to other countries. The working relationship between Mr. Bush and President Gorbachev has grown increasingly easy and relaxed since the Malta summit in December of 1989, which started off with what national security adviser Brent Scowcroft calls "a certain amount of stiffness and formality." Another White House official describes the relationship as one where the two leaders can frankly discuss even unpleasant subjects. Bush is likely to bring some kind of friendship offering on the economic front. It is not likely to be support for the full World Bank and International Monetary Fund membership that Mr. Gorbachev asked for last week. But it may well be an announcement that Bush will submit a US-Soviet trade agreement to Congress. The trade agreement is a prerequisite for granting the Soviets most-favored-nation trade status. The agreement was signed by Bush and Gorbachev a year ago in Washington. Bush held back from submitting it to Congress for ratification, however, until the Soviets liberalized their immigration laws in May. By then, another snag had arisen. The Soviets were pirating American movies, airing "Die Hard 2" on government television without permission or royalties, for example. Reportedly, the two countries are nea r agreement on protecting intellectual property rights, including those of moviemakers and artists. The trade agreement will not immediately boost Soviet exports to the US because oil is the only significant Soviet product with an American market. But it opens long-term possibilities for trade to develop by cutting tariffs into US dramatically, notes Robert Cullen, editor of Soviet-American Trade, a newsletter. Bush will spend most of his time with Gorbachev, who Bush sees as "very much the man in charge," says an official. He will also meet with Boris Yeltsin, the maverick president of Russia, the largest Soviet republic. And he plans to meet with Eduard Shevardnadze, the former Soviet foreign minister who was instrumental in transforming superpower relations until he resigned last year in protest against Gorbachev's shift to the right. In Kiev, Bush will address the Supreme Soviet of the Ukraine, the first time an American president has ever addressed the governing body of a Soviet republic. With these meetings, Bush can show some support for the aspirations of the republics and for democratization in the Soviet Union. At the same time, he can avoid undermining Gorbachev, who still represents stability. Although the Bush administration has no official opinion of the draft union treaty forged last week between nine republics and the central Soviet government - a treaty that seemed to hand much power to the republics - the White House is clearly pleased with the treaty's direction.