West Germany's ruling coalition won a narrow but crucial victory yesterday in state elections in Hesse, where a local defeat could have led to the fall of Chancellor Helebut Schmidt's federal government in Bonn.

Early returns and computer projections indicated that the ruling coalition of Social Democrats and free Democrats would get an absolute majority of 50.8 per cent in the new state legislature and thus retain control of the state's votes in the parliament in Bonn.

Opposition Christian Democrats and their sister party in Bavaria, the Christian Social Union, already control six of Germany's 10 states and thus have a majority in the upper house of parliament, where states are represented. A victory in Hesse would have given them a two-thirds majority and power to veto legislation put forward by Schmidt.

Washington Post correspondent Michael Getler reported that while the election was a setback for consevatives, the vote nevertheless reflected strong conservative feeling in a state that has long been a stronghold of the center-left Social Democrats.

The balloting was regarded as a personal triumph for the jovial Social Democratic state governor, Holger Boerner, who has restored much of the prestige the party lost when it was embroiled in political and banking scandals two years ago.