Jubilant Democrats, bolstered by overnight poll results, claimed victory for Walter F. Mondale in Sunday night's debate, while Republicans countered that Mondale failed to get the "knockout" he needed to close President Reagan's wide lead in the polls and go on to win Nov. 6.

Democrats universally appeared to believe that Mondale had made his strongest and most effective television appearance ever, while Republicans conceded that Reagan was off his form, appearing "hesitant" and sometimes nervous with occasional lapses of memory, and that he made a weak closing statement.

Every overnight poll taken except the one for Reagan's campaign showed Mondale as the winner by as much as 20 points. None showed any movement in voter intentions yet, but Mondale's campaign manager, Robert G. Beckel, predicted the Democrat will start closing the gap within the next week.

A Newsweek poll of 379 registered voters who watched the debate had Mondale as the winner, 54 percent to 37 percent -- almost exactly the lead Reagan has over Mondale in the latest Washington Post-ABC and Gallup polls.

Peter Hart, Mondale's pollster, interviewed 600 viewers Sunday night after the debate and found Mondale the winner, 52 percent to 32 percent.

An ABC News poll, however, showed Mondale as a narrow victor, 39 percent to 38 percent.

Reagan's poll indicated that the president won with 41 percent to 38 percent for Mondale, with more than half the respondents indicating they would vote for Reagan.

A CBS-New York Times poll had Mondale winning 43 percent to 34 percent, while USA Today's poll gave Mondale a 39 percent to 34 percent margin.

While some Democrats, such as New York campaign consultant David Garth, predicted that the electorate is "going to move big" between now and Election Day, most cautioned that Mondale's strong showing just gave him a boost and an opening that he still has to exploit.

"Mondale has to gain 5 points out of this in the next week," said Robert Squier, who is working on a number of Democratic Senate races. "He has to take the debate into the future, talk about what he's going to do and look at the role of government in our lives. He's got to take it to new tech. The worst thing he could do is to try to glue together the old Democratic programs."

Some Democrats voiced unease about Rep. Geraldine A. Ferraro's scheduled debate with Vice President Bush on Thursday night.

"If she comes on too strong, she could be negative," Garth said of the Democratic vice presidential nominee. "I hope she won't feel the need to outdo him Mondale , try to knock it out of the park when all you need is a base on balls."

"Mondale did all right in a skirmish," said a Republican strategist. "But he still has a 20-point deficit to make up and I still don't see how he gets 270 electoral votes even if he wins states he should like New York, Pennsylvania, Massachusetts and Rhode Island. How does he break into the South and West?"

Ironically, the polls indicate that Mondale won the debate primarily on his style and personal presentation, whereas Reagan won on the issues -- the opposite of the widespread judgment that Reagan is all style and no substance.

Hart said that respondents in his polls praised Mondale for "style, presentation, leadership" and called him "clear, straightforward, at ease, in command, realistic, sincere."

"All the negative comments related to issues," Hart said. "By contrast, all the positives for Reagan were issue-oriented and negatives primarily related to style -- hesitant, nervous, confused, incoherent, lacking confidence, evasive."

Some Democrats contended that Reagan's sheltered "Rose Garden" strategy has insulated him from contact with voters and reporters and as a result he was "rusty" in his 90-minute encounter with Mondale.

Some also suggested that Reagan's performance made his age an issue and some Republicans privately worried that they were right.

"Reagan showed his age," said Rep. Tony Coelho (D-Calif.), chairman of the Democratic Congressional Campaign Committee. "The age issue is in the campaign now and people like me can talk about it, even if Mondale can't."

"I thought the only thing Mondale could do was to put the wimp issue aside and get himself in the ball game," said one Republican professional. "But he raised the question of whether Reagan's too old, whether he's up to another four years."

Some criticized Reagan for playing Mondale's game of "number-crunching" and reciting details of programs.

"He used a lot of eye-glazing facts and figures," said Terry Dolan, head of the National Conservative Political Action Committee. "Gone was the vision of the future that he put forward in 1980. He was using statistics that made no sense."

Garth predicted that the media will amplify the story and that Mondale may be within 10 points of Reagan by the time of their second debate Oct. 21.

"The young people are reacting to the age and the 25 percent of the Democrats who were for Reagan have to see that this Democrat is a decent, classy guy they can support," he said.

Sen. Gary Hart (D-Colo.), who challenged Mondale for the nomination, predicted that the under-45 "Yuppie" vote will "turn massively in the next 30 days" to the Mondale-Ferraro ticket because of the debate.

Others were more cautious, however.

"It wasn't a Mondale knockout and I don't think it will close the gap at the polls but it will narrow the gap," said Montana Gov. Ted Schwinden (D).