SUDDENLY, the breakup of the Soviet Union has handed the Bush administration a real chance to get serious about preventing the spread of nuclear weapons.The USSR's collapse could lead to the birth of new nuclear-armed states, most likely the Ukraine and Kazakhstan. If these nations go nuclear, ethnic tensions and political instability will be dangerously exacerbated. More broadly, global efforts to halt nuclear proliferation would be undercut. This alarming prospect need not come to pass. A concerted Western effort to stop this potential proliferation could ease the gravest international issue arising from Soviet disintegration. At the same time, a tough Western stand would deter would-be proliferators elsewhere. Regrettably, George Bush's recent speech on nuclear arms missed an opportunity to warn the republics directly on nuclear weapons. Moreover, it is no longer clear that Mikhail Gorbachev will have the authority to make good on his pledge to scrap or withdraw the tactical nuclear weapons in the republics. At the moment, it is unclear whether the Ukraine and Kazakhstan ultimately will claim the sizable portions of the USSR's atomic arsenal stationed on their territories. For now, the 27,000-warhead Soviet stockpile remains under central control, where it is subject to elaborate safeguards against unauthorized launch, theft, or misuse. Yet politicians in both the Ukraine and Kazakhstan are sending mixed signals about their nuclear intentions. Even if such proliferation seems unlikely, the mere possibility calls for the West to establish firm opposition now. Ukrainian leader Leonid Kravchuk has reportedly assured President Bush that he wants a Ukraine free of nuclear weapons once it has gained full independence. But that hopeful statement cannot be accepted at face value. Mr. Kravchuk himself, an opportunistic ex-communist who made a late conversion to the nationalist cause, has given vague and somewhat contradictory responses when quizzed about the Ukraine's nuclear intentions. Last year the Ukrainian parliament passed a nuclear-free declaration, and initially after the coup Kiev indicated that the weapons should be removed, presumably to Russia. However, Rukh, the Ukrainian nationalist movement that may dominate politics after coming elections, has objected. Some Rukh officials feel that the Ukraine would be comparatively weakened if the weapons are moved to Russia, a historical rival. Ukrainians were understandably worried by a warning from Boris Yeltsin's Russian government that breakaway republics could not assume that current borders with Russia would remain unchanged. The Ukrainians now believe that nuclear weapons on their soil will be useful bargaining chips in independence talks with Russia and the central government. More ominously, some Ukrainian political figures suggest that nuclear forces will afford their country instant great-power status. IN the Central Asian republic of Kazakhstan, meanwhile, the government also reiterated its antinuclear position after the coup in Moscow failed. But lately, Kazakh leaders are backtracking. They have rejected proposals to move nuclear weapons to Russia and want joint Kazakh control over the weapons. Certainly, neither the Ukraine nor Kazakhstan has the command and control structure, the technical expertise, or the political maturity to handle nuclear weapons safely. With its vast land area, population of 52 million, and proven industrial capacity for building atomic warheads and missiles, a nuclear Ukraine passing through a period of economic depression and political instability would cast a long shadow over the newly democratizing states of Eastern Europe, and pose genuine security concerns for Western Europe and NATO. It is also not difficult to imagine an authoritarian Kazakh regime of the future becoming a regional strongman, throwing its nuclear weight, for instance, behind fellow Turkic-speaking Muslims in Azerbaijan at war with Christian Armenia. In a region where Islamic fundamentalism is growing and prospects for democracy seem poor, this largely undeveloped nation could prove to be an unstable home for atomic weaponry. The Bush administration can do much to forestall this potential danger. First, it can move s wiftly to unify the Western industrialized countries against suggestions that republics might gain the bomb. A common stand could break any republican temptation to keep the weapons. The West now enjoys both considerable moral authority and leverage with the Ukraine and Kazakhstan. They are entering a painful transition to mixed economies, and they badly need Western financial and technical help. The West should deliver a blunt message: Keep your nukes and lose our aid. Second, if these nations become fully independent, the West must encourage and, if necessary, pressure them to sign the Nuclear Non-Proliferation Treaty and other arms-control accords previously signed by the USSR. Finally, the Bush administration should broaden the unilateral arms cuts it proposed, enabling the Soviets to match US moves. The elimination of all tactical nuclear weapons should be the immediate goal. These weapons are deployed widely in the USSR and are subject to fewer safeguards; they are thus the most vulnerable to expropriation by breakaway republics. Parallel negotiations on slashing strategic intercontinental ballistic missiles should also begin anew. In a dissolving Soviet Union, destroying missiles and warheads will ease the greatest risk now confronting the West: their use by the republics or others.