Spaniards awoke today to face the question of whether the Socialist government they have just elected will be able to deliver on its promises of change for the better without antagonizing Spain's traditional power brokers in the conservative business and military establishment.

For the victorious Socialist leaders, there is an additional anxiety: Can a government formed of young, inexperienced and largely unknown middle-class professionals, already loathed by a large and strong minority of its citizens, mistrusted by some of its overseas allies and containing potentially dangerous divisions within its own ranks, endure?

The Socialists' winning margin was as decisive as predicted. The latest figures, likely to undergo minor adjustments before becoming official next week, gave them an overwhelming majority, with 201 of 350 congressional seats. With an unprecedented 78 percent of the 27 million electorate voting, the right-wing Popular Alliance won 106 seats and a strong opposition role that leader Manuel Fraga said would be "more than merely verbal."

Although under the Spanish constitution it may be more than a month before the Socialists are called to form a government and elect party leader Felipe Gonzalez premier, the Union of the Democratic Center that has run democratic Spain since the death of dictator Francisco Franco in 1975 has become the lamest of ducks.

Among the 157 UCD seats lost yesterday, leaving the party only 11 in the next government, were those of current Premier Leopoldo Calvo-Sotelo and more than half his Cabinet, including the ministers of defense, treasury and foreign affairs.

There is a Spanish saying about Christopher Columbus' discovery of the New World that Ramon Trias Fargas, a Catalan nationalist leader, recently applied to Gonzalez' spectacularly short rise to fame and power. "When he left, he didn't know where he was going. When he got there, he didn't know where he was, and when he got back, he didn't know where he'd been," he said.

Gonzalez surely knows where he has been -- 13 years underground, trying to reorganize a party that Franco first decimated during the 1936-39 Civil War and then declared illegal. But where he decided to go, and whom he has taken with him on the trip, are largely uncharted territories to much of Spain and the world.

Of the 201 elected Socialist deputies, at least 60 percent are incumbents from the current parliament, in which the Socialists hold 128 seats. They, and those who will join them in the new majority, are far from the workers and peasants whose votes this time greatly contributed to their victory.

Like their French Socialist counterparts, the elected representatives of the new Spanish majority come overwhelmingly from the middle and upper middle classes -- university graduates, teachers, lawyers, engineers. "There are practically no blue-collar workers," said Gonzalez campaign manager Julio Feo. "They are more active in the labor movement" within the General Workers' Union federation that is one of the Socialists' power bases.

But there the comparison to the French largely ends. The difference between them is the difference between French President Francois Mitterrand, whose long, sophisticated history in government matches his party's more traditional rise to political power, and Gonzalez, the casually spoken and dressed product of the 1960s.

Although the Socialist Party is the oldest in Spain, the program and image that won in yesterday's elections are a far cry from those of the doctrinaire workers' party formed in Madrid in 1879. Its change, and its ascension to majority government, are purely the work of Gonzalez, his sidekick -- his Rasputin, according to some in the party -- Alfonso Guerra, 42, and a handful of university friends.

During the 1960s, the old Socialist leadership -- thrown out by Franco after the civil war -- sat in exile across the Pyrenees in Toulouse.

Guerra, a former teacher turned bookseller, and Gonzalez, the friend from his hometown and university in Seville in whom he saw charisma and leadership abilities, crisscrossed Spain in a battered Renault contacting pockets of leftists and trying to rebuild the party underground.

In 1975 the "Seville Mafia," with the help of some like-minded young graduates of Madrid's university, wrested power from the aging Toulouse leadership in a secret party congress outside Paris. Gonzalez was elected party secretary, and after Franco's death entered the mainstream of European Democratic socialism as leaders like Mitterrand, Willy Brandt and Olof Palme of Sweden traveled to Madrid to endorse him.

In Spain's first post-Franco elections in 1977, the Socialists won 118 seats. It was a reflection, British-trained sociologist Jose Maria Maravall, 40, later wrote, less of Spain's new burst of freedom and old civil war battles than of the traditional Spanish "allegiance to the left and right [that] survived through 40 years and [was] transmitted intergenerationally in families and communities."

The task of the party during the next several years, according to Maravall, was to recover the working-class vote that had been lost to rightists who preached stability and anticommunism, and to convince Spain that the new young leaders were capable and moderate enough to lead the country.

One of the first steps came in 1979, when Gonzalez won a hard-fought battle against the party left to have the word Marxist dropped from its name. That year, Guerra masterminded an electoral campaign centered on a newly serious, dark-suited Gonzalez who spoke of responsibility. They added only three seats but convinced the electorate the Socialists could act as a responsible mainstream opposition.

Meanwhile, the party ranks were swelled with defections from the increasingly doctrinaire and obsolete Spanish Communist Party, and the fast-collapsing center that had held the country together after Franco. By this summer, the Gonzalez-Guerra team was ready to press for victory on a platform that was remarkably short on ideology and specifics and long on a general call for ethics, moral rearmament and a "change" that post-Franco Spain finally was ready for.

The campaign was not hurt by the fact that the Socialist candidates, from Gonzalez on down, were primarily young, energetic, attractive and the virtual antithesis of the monied, rightist political elite that represented the past.

Although Gonzalez will likely accept the resignation of most current Spanish diplomats and high-level civil servants, he has vowed that party affiliation will not be a requisite for spots in the new administration and has extended an olive branch to others.

Among those likely to hold Cabinet posts are Maravall, as education minister, and Javier Solana, a 40-year-old physics professor who did postgraduate work at the University of Virginia after being expelled from studies here under Franco, as minister of industry and energy.

Mentioned for treasury minister is Francisco Fernandez Ordonez, 52, a Harvard graduate who served as finance and justice minister in previous governments and describes himself as a social democrat. Among those rumored for foreign minister, the top candidate appears to be Fernando Moran, a fiftyish career diplomat who, like many middle-level leftists and liberals, managed quietly to survive under Franco.

Most of the members of Gonzalez' economic team are known as moderate technocrats who hope, against the prediction of Spain's conservative business and banking leaders, to lower both unemployment and inflation in the next four years.

While Gonzalez will not have to contend with militant Communists within his government, as does Mitterrand, the first test of party unity is likely to come in January when a party conference scheduled to discuss internal reforms demanded by what are called the "leftist socialists." About 20 to 25 percent of the party activists, they want to "modify the party statutes to recognize the two currents," according to Manuel de la Rocha, 35, mayor of the Madrid suburb of Fuenlabrada.

The leftists want not only proportional representation, rather than the current majority-take-all, within party organs, but firm statements on "the elimination of classes . . . and getting out of NATO."

Gonzalez has tried to avoid characterizing Spain as a forum for class struggle, arguing that its social and economic positions are not ready for it. He has been vague about the timing for his promised referendum on NATO.