BELGRADE, NOV. 23 -- Serbia's major non-communist opposition parties announced today that they would boycott its first postwar multi-party elections next month, leaving the communists in control of Yugoslavia's most populous republic.

The 12 opposition parties, in a joint statement, accused the communists of planning to deny them victory in the Dec. 9 election by fraud and ballot-rigging. Several of the parties, particularly the radical nationalist Serbian Renewal Movement, had been expected to do well, perhaps even ousting the communists, who have renamed themselves Socialists.

Serbia and its smaller neighbor, Montenegro, will be the last of Yugoslavia's six republics to hold multi-party elections this year. The outcomes of these elections will be critical in determining the future of this multinational federation of 23 million people, with the leaders of northwestern Slovenia and Croatia, elected last spring after four decades of communist rule, seeking to reduce Serbia's dominance by pressing for a looser form of confederation.

In the key central republic of Bosnia-Hercegovina, where Serbs, Croats and Moslems -- recognized here as a separate nationality -- form a volatile mixture that mirrors the country's diverse makeup, final results from Sunday's election, made public today, showed a humiliating defeat for the communists.

Three nationalist parties representing the Moslems, Serbs and Croats won 97 of the 130 seats in the main chamber of parliament, with the communists finishing fourth with only 13.

The Moslem, Serbian and Croatian nationalist leaders are now holding talks on forming a coalition government for Bosnia, which is Yugoslavia's third biggest republic with a population of 4.2 million. While the Bosnian communists' defeat had been widely predicted, the sudden reconciliation among the competing nationalists came as a surprise. Until two weeks ago, the nationalist parties were bitter opponents, trading accusations and even predictions of civil war.

Bosnia's nearly 2 million Moslems, a legacy of five centuries of Turkish rule, were given the status of a nation in the 1970s by Yugoslavia's charismatic postwar communist leader, Marshal Tito, to create a buffer nation between Serbs and Croats.

The leader of Bosnia's mainly Moslem Party of Democratic Action, Alija Izetbegozic, called on the republics to create a new Yugoslavia, forging a "historic compromise" between the united federal state advocated by Serbia and the looser confederation demanded by Croatia and Slovenia.