AS Japanese newspaper headlines eagerly anticipate the end of 38 years of Liberal Democratic Party (LDP) rule, the excitement is understandable. An opposition-led coalition government will be something new in Japan. A socialist government was elected in the 1940s but it was brought down by parliamentary manoeuvre. This will be the first time that Japanese voters have directly voted a government out of office, at least since 1945. But it has not happened yet and there are several hurdles remaining. First, the summit meeting of seven opposition leaders due to be held in Tokyo today will have to overcome some wide differences in policy. For instance, the Japanese Socialist party recognises North Korea, while the other six opposition parties all go along with Japan's longstanding diplomatic recognition of South Korea, but not the North. Their best option would be to stress that they are only coming together to eliminate the political corruption which has become the LDP's trademark, and to institute reform of the electoral system. They could even announce that once this is accomplished another election will be held under the new system. In that way, they would remove the pressure to achieve an almost impossible unity right across the political spectrum from the Shinseito (Japan Renewal Party) on the right, to the Japan Socialists on the left. The seven parties have expressed their determination to get the reform bills passed before the end of the year. This is because the House of Representatives has to turn to discussing and passing the budget in the first quarter of 1994. The budget debate seems certain to heighten the political differences within the seven-party coalition and may bring about its downfall. Second, and more immediately, the coalition has to chose one leader as its prime ministerial candidate in the voting due to take place in the House of Representatives on August 6. But the third and most difficult hurdle remains the wafer-thin majority of the seven parties. At the moment (after a few post election shifts in loyalty), the Socialists have 70 seats, followed by Shinseito (56), Komeito (51), Democratic Socialist Party(15) and Social Democratic Union (4). The five original members of the opposition coalition thus have a combined strength of 196 seats. The combined strength of Nihon Shinto (36) and Sakigake (13) is 49, but that leaves the seven party coalition, with 245 seats, still eleven short of a simple majority. Were the communists 15 seats added to the total, the coalition would have a majority, with 261 seats. But the Cold War still pervades Japanese domestic politics - no one has yet talked of making the communists a coalition partner. So the coalition can only get its majority either through more rapid defections from the LDP, or from among the 27 ''independents''. Once the coalition has strengthened its togetherness, it will have to set about winning over roughly two-thirds of the independents whose support will be required not just for the prime ministerial contest next week, but also for the battle over reform bills that will follow.