LIBERIAN faction leaders, vowing to end six years of civil war, signed a peace accord in Nigeria that promises a cease-fire and democratic elections within a year. It's a step deserving praise, but cautious praise, since 12 earlier accords failed. At this early stage, the agreement seems to have a fighting chance. Previously, faction leaders disagreed on how to divide up power. This accord tries to rectify the problem by giving the leaders shares of power on a six-member Council of State, which will oversee the country until elections. The accord will work, however, only if the warlords-turned-politicians are serious about participating in elections and persuading 60,000 rebel fighters to lay down their arms. If any of the leaders balk, the stage is set for anarchy in Monrovia, Liberia's capital, which is under peacekeeper control. Whether peace holds depends largely on one man, faction leader Charles Taylor, who started Liberia's war with a rebel invasion in 1989 and is partially responsible for the failure of earlier peace talks. Now Mr. Taylor says he will participate in elections and, if unsuccessful, will accept the loss as ''a wish of the Liberian people.'' Time will tell if he keeps that promise. Success also depends on the United Nations and African peacekeeping countries. The factions signed the accord under threat from the UN that it would end its mission if there was not a peace plan in effect by Sept. 15. The eight African nations with peacekeeping soldiers in Liberia also say they won't continue their costly mission there if the fighting continues. But now is not the time to pull out. Liberia can't afford to lose either foreign aid or the measure of security peacekeeping forces provide. The next step is to set a date for elections. Voter registration alone will be a problem in a country where half the population is displaced. Liberia, as well as neighboring Nigeria, which has tried to act as broker, has little experience with free and fair elections. This is where Western democracies can play an important role. Liberia, America's stepchild in Africa, has taken the first step toward a peaceful settlement. It is going to need all the help it can get to continue.