Voters here have approved the future use of nuclear power for their city, in the first referendum in the nation on the issue since the Three Mile Island nuclear reactor accident.

The Saturday vote was a stunning defeat for anti-nuclear forces, who had hoped for a sizable defection to their cause from the city's affluent white voters after the reactor accident in Pennsylvania.

Complete but unofficial returns show that a proposal authorizing the city council to sell more than $215 million in revenue bonds by the city-owned electrical system to finance further construction of the four-city South Texas Nuclear Project passed by a 53.1 percent majority.

Another proposal authorizing the city council to sell Austin's 16 percent share in the project failed by a much narrower 50.9 percent margin.

The lead in both votes changed hands repeatedly throughout Saturday night's counting and a one point it appeared that both pro-and anti-nuclear proposals might be approved.

However, a final surge of votes from affluent precincts in the city's Northwest side, which voted pro-nuclear by 65 percent or better, gave the pro-nuclear Committee for Economic Energy a clear-cut victory.

Perhaps no one in Austin was more surprised by the victory than the committee's campaign manager, John Rogers. While the polls were still open Saturday afternoon, Rogers had gloomily predicted defeat by a 58 percent vote or more.

He said a series of last-minute radio and television ads by Austin's popular mayor, Carole McClellan, was a decisive factor in the pro-nuclear victory.

"Obviously some minds were changed by something, and it had to be McClellan," Rogers said. He said that polls taken after the Three Mile Island accident had shown anti-nuclear sentiment appeared to be growing among women voters, who were McClellan's strongest supporters.

About 200 anti-nuclear activists also acknowledged McClellan's role, booing her from the auditorium of the city electric system offices when she came to discuss election results with reporters Saturday night.

"This was one of the toughest political decisions I have ever made," said McClellan, who won election to a second term Saturday night with nearly 79 percent of vote.

"In the wake of the Harrisburg accident, I reexamined every aspect of my position, and I did it as a mother, not as mayor," she said. McClellan has four children.

"Even with the seriousness of the Harrisburg accident, at least it appeared that the safeguards worked," she said. "You have to weigh the costs and benefits."

McClellan and anti-nuclear organizers both agreed that the Three Mile Island accident had less effect on the referendum than did local issues.

"I think Austin voters understood the needs for energy diversity," she said, referring to the city's near total dependence in the past on the Lo-Vaca Gathering Co., a supplier of natural gas, for fuel to generate its electricity.

During the winter of 1972-73, the company ran short of natural gas, prompting Austin's 1973 decision to enter the South Texas Nuclear Project.

But construction cost overruns on the two 1,200-megawatt nuclear reactors being built in coastal Bay City, some 150 miles from Austin, created widespread anti-nuclear feeling.

The price tag on the project, now scheduled for completion in 1983, has doubled to $2 billion since 1973. Construction is also being funded by San Antonio's city-owned power system and by private utilities in Houston and Corpus Christi.