SOVIET President Mikhail Gorbachev and United States President Bush will meet today for the first time since August, when a failed coup led to a sweeping anti-Communist revolution in the Soviet Union.The agenda for their brief meeting in Madrid, before the two men open the jointly sponsored Middle East peace conference tomorrow, is a crowded one. Aside from the Middle East conference, the two leaders are expected to talk about economic assistance to the Soviet Union and about controls on nuclear weapons. During the past month, the two presidents have exchanged groundbreaking proposals to eliminate tactical nuclear weapons, to stand down from a nuclear alert status, and to move toward a new era of strategic nuclear-weapons stability. But beneath all these issues lies an unstated question that will dominate all others: the future of the Soviet Union itself - whether it will remain a united nation with a major role to play in world affairs. (Russian president floats radical reform bid, Page 6.) Mr. Gorbachev has already been confronted with those questions, outlined in a brief interview published yesterday in the Arab newspaper Al-Sharq Al-Aswat. "Of course, our country is now experiencing great difficulties, which are inevitable at the stage of such immense and radical transformations," Gorbachev responded. "But all talk about a decline of our role in world politics contradicts facts, including the fact that our country is cochairman at the Middle East peace conference." The old Soviet Union may no longer exist, Gorbachev added, but "a new union, the union of sovereign states, is in the throes of being born." Despite such confidence, it is valid to ask what role, if any, will the Soviet Union play in world affairs. Until his departure yesterday, Gorbachev's trip attracted little attention here, with barely a mention in the Soviet media. "Everybody is preoccupied with the domestic situation, too preoccupied," comments Vitali Naumkin, deputy director of the Institute of Oriental Studies. "But for Gorbachev it is important - it is an event that proves that in this crucial period, a union foreign policy does exist." Still, the preparations for the Middle East conference have been entirely the province of the Soviet Foreign Ministry. "[Foreign Minister Boris] Pankin and his team of experts are traveling around as if we are living in the good old days," says Mr. Naumkin, a leading Soviet Middle East specialist. While giving credit to US Secretary of State James Baker III for getting the conference off the ground, Soviet experts argue that the conference is the result of the joint activity of both countries over a long period of time, beginning with the original Soviet proposal for the gathering. In that sense, "both presidents deserve the ceremonial cochairmanship," says Vladimir Lukin, head of the Russian republic's parliament foreign affairs committee and a member of the Soviet delegation. The issue of whether or not a Soviet Union exists also plagues prospects for economic aid from the West. On Saturday, senior officials from the 12 republics of the former Soviet Union met with the chairman of the committee managing the Soviet economy, Ivan Silayev, and his deputy, radical economist Grigory Yavlinsky. Just back from the International Monetary Fund meeting in Bangkok, Mr. Yavlinsky told republic leaders that Western governments were not prepared to throw new funds into the Soviet Union until the republics agreed to honor the Soviet Union's almost $70 billion foreign debt. He argued against the idea, widely promoted by the Ukraine and others, of dividing Soviet debt and reserves of currency and gold. Those participating in what remains of the Soviet central government clearly hope to use foreign pressure to force the republics into greater economic cooperation as called for in the treaty of economic union signed by eight of the 12 republics in mid-October. On Sunday, republican representatives began meetings here to discuss financial aid with representatives of the Group of Seven leading industrial nations. Gorbachev may be looking for Bush to apply some indirect pressure on the republics in another crucial area as well: control over nuclear weapons. The Ukrainian announcement last week of plans to form a 400,000- to 500,000-man army has underscored fears that the Soviet nuclear arsenal could be divided among several republics, although the Ukrainian parliament pledged support for central control of those weapons. The US and Soviet leaderships now share a common interest in the centralized command of nuclear weapons, argues Sergei Rogov, the senior military specialist at the USA-Canada Institute. According to the expert, the Ukrainians not only have missiles deployed on their territory, they also manufacture SS-18 and SS-24 intercontinental ballistic missiles in factories located there. If it wanted to, he says, the Ukraine would be capable in a few years of producing nuclear warheads as well as missiles to delive r them. "In this situation, it is not the Russian-American nuclear balance but the Russian-Ukrainian balance which becomes the dominant issue," says Mr. Rogov. The Bush arms initiative, along with the Gorbachev response, provides an opening to eliminate the republican-based nuclear weapons as part of steps to eliminate multiple-warhead missiles, he says. In effect, Bush and Gorbachev "could cook a deal to allow the two countries to say that all the weapons on your territory belong to a category fully eliminated," Rogov says.