After a costly political drift toward the left that fractured the party and alienated voters, West Germany's opposition Social Democrats are assuming a more moderate profile in pursuit of a broader electoral base that could challenge Chancellor Helmut Kohl's ruling center-right coalition.

The centrist faction in the party received a big boost when Johannes Rau, the popular premier of North Rhine-Westphalia, led the Social Democrats to a resounding victory in state elections May 12. The outcome confirmed Rau as the most likely party candidate to run against Kohl for chancellor in the March 1987 national elections.

While antinuclear sentiment is still predominant among left-wing Social Democrats, Rau's strong showing in the country's most populous state, where one-third of the West German voters live, vindicated the arguments of party moderates who insist that Kohl's government is most vulnerable on economic, not security, issues.

As a result, party strategists are crafting new political appeals for the next campaign based on jobs and new technologies, rather than opposition to U.S.-built nuclear missiles. But the debate between party factions could grow more heated as the moderates try to shove the party further right.

"Anyone who believes that unemployment and the government's errors will automatically bring the Social Democrats into a majority is mistaken," says Peter Glotz, the party manager and a leading moderate. "This party must change even more if it wants to win" in 1987.

Apart from policy disputes, the Social Democrats believe that the populist appeal of Rau is guaranteed to lure lost voters back to the party.

Rau, 54, the earthy son of a pastor, enjoys ardent support from the party's traditional sources of political power -- the churches and the trade unions. He is known as a pragmatic populist whose policies do not deviate much from the party's mainstream views, advocating broad social welfare benefits and worker participation in economic management.

On foreign and security issues, Rau says he is a staunch supporter of the Atlantic Alliance and the European Community and spurns the unilateral disarmament views that have taken root among left-wing Social Democrats and the radical, antinuclear Greens party.

He is not considered an original or compelling political thinker, but he shines on the campaign stump. He shuns turgid policy discussions and prefers to win over his audiences with his homespun, yet eloquent, rhetoric that is liberally laced with jokes and anecdotes.

"Brother Johannes," as he is fondly called by friends and constituents, is a leading council member of the Evangelical, or Protestant, church, which long has played an important role in German politics. The church, which commands large support in East Germany, exerts great influence in East-West dialogue and arms control issues.

Three years ago, Rau married Christine Heinemann, 26 years younger than him and granddaughter of the late Gustav Heinemann, president from 1969-74. Rau now extols the virtues of family life with his wife and two children, and has managed to gain more political capital in a country where the plunging birth rate, the world's lowest, has prompted alarms about "Germans dying out."

Rau proudly displayed his family on posters and capitalized on his title of "father of the year." The pitch was so effective that Martin Bangemann, leader of the government's junior partners, the Free Democrats, complained: "How can you fight a political battle when two babies serve as the electoral argument?"

His cheerful, upbeat personality also holds refreshing appeal for German voters used to dour politicians. His "man of the people" image is enhanced by his habit of sitting down at a tavern in Wuppertal, his hometown, to play the card game skat with all comers.

Rau now appears set to succeed the lackluster parliamentary leader, Hans Jochen Vogel, as the party's next candidate for chancellor at a special congress in December. Even so, his struggle to win the party's soul is likely to continue with his younger rival, Oskar Lafontaine, 42, state premier of Saarland.

Both men succeeded in capturing absolute majorities in their states this year while keeping the radical Greens below the 5 percent required for a seat in parliament.

They also preside over the country's two main "rust belts," where deteriorating steel mills and exhausted coal mines have caused joblessness to soar.

A fiery orator who espouses removing West Germany from NATO's military structure and banning nuclear weapons on its soil, Lafontaine proposes to regenerate the Saarland's weak economy through "ecosocialism," an offshoot of the "small is beautiful" philosophy, in which workers would be channeled into artisan jobs in small enterprises that do not pollute.

His views, popular among young people as well as desperate, out-of-work coal miners, have coopted many potential supporters of the Greens party, which received less than 3 percent of the vote in state elections last March.

Rau, on the other hand, disdains the ideas of the Greens and flatly rules out forming a working coalition with them. As the standard bearer of his party's old line, he sticks to the belief that rejuvenation of the factories could take place with the right mix of state aid and investment in new technologies.

Among Social Democrats, it was widely believed that only Lafontaine's approach of robbing the Greens of their issues could succeed in forging a "majority to the left" of Kohl's government. Party Chairman Willy Brandt, an admirer of Lafontaine, has been a strong proponent of this thesis.

But Rau's surprisingly good showing has changed many minds within the party and fortified the claims of party moderates, who contend that the vast bulk of German voters are in the center and do not want to tamper with radical policies proposed by the right or the left.

After Rau's victory, a national survey by the Wickert Institute showed the Social Democrats ahead of the ruling Christian Democrats for the first time since the 1983 election. Of those questioned, 44 percent said they would vote in the next national elections for the Social Democrats and 41 percent said the Christian Democrats. The Free Democrats received 8 percent and the Greens 6 percent.

Despite such dramatic gains, the Social Democrats are still far removed from power because the center-right coalition is still likely to achieve a majority.