The stock market crisis represents a significant setback for the Republican Party, undermining the GOP's claim that it is best equipped to handle the economy, according to a number of political scientists and political analysts.

"The Republican Party has lost the chance it had to establish a lasting advantage on the prosperity issue. They had that chance," said Martin Wattenberg, of the University of California and author of "The Decline of American Political Parties."

"What this all comes down to is that we are not going to have a majority party in presidential elections. The net result of the Reagan era will be to wipe out the Democratic advantage, but not to establish the Republican Party as the new majority party," he added.

Just three years ago, Thomas E. Cavanagh and James E. Sundquist wrote an essay published by the Brookings Institution suggesting that voting patterns in the 1984 election pointed strongly toward the likelihood of sustained Republican gains. "Public opinion data . . . support the thesis that something historic is indeed happening to the party system. The Republicans have approached parity with the Democrats, finally establishing a genuine two-party system," they said.

Interviewed after the markets closed on Friday, Cavanagh said the precipitous price decline and subsequent market vacillations are "going to make a lot of people who believed it was morning again in America question their faith." He added that much of the movement to the GOP "was based on the assumption that Republicans know how to manage the economy. This {the market fall} has taken away the main rationale for the people who have switched to voting for the Republicans."

Everett Carll Ladd, an expert on polling and a professor at the University of Connecticut, was less willing to draw a firm conclusion until there are clearer signals of the direction of the stock market and the economy, but he stressed the importance of domestic economic success for the growth of the GOP.

"The whole question of the government role in the management of domestic matters has been a very big piece of the recent political experience," he said. "Anything that would happen to significantly change that picture would be consequential."

John Petrocik, a political scientist at the University of California Los Angeles, said that a modest decline in the stock market would "not be a major problem" for the GOP but that "if we get a major recession, then obviously the Democrats are going to have a runaway."

Walter Dean Burnham, of the Massachusetts Institute of Technology, said, however, that recent months have been like a "slow-motion train wreck" in the Reagan administration, and the stock market problems "bring to an end the Reagan 'feel-good' era . . . . There is a lot going wrong in Reagan's presidency. Pretty clearly, cumulatively, it's the end of an era."

Warren Miller, head of National Election Studies and professor at Arizona State University, said the market decline "could be fairly devastating . . . . It's bound to tarnish the image of a domestically very successful administration."

Miller said Republican gains in party identification among voters "have been a function of the candidacy of Reagan and the bland background of nonevents. Then, all of a sudden, it turns out that the fears of the trade imbalance and of the national debt have the appearance of being justified."

People who have switched to the GOP, Miller said, tend to be men and women who are not politically active but who are drawn to President Reagan on the basis of his personality and style. "I think it {the stock market crisis} makes it {the GOP trend} difficult to continue and the Republican hold on them {the swing voters} is very tenuous to begin with," he said.

Thomas Mann, director of government studies for the Brookings Institution, said that even if there is a full recovery on the stock market, the damage to the GOP will remain.

"I think the early readings that I've seen tell me that you could now have a full recovery and an avoidance of recession and it would still have some lasting effects. It gives substance to the Democratic charge that all is not well in the Reagan era, it gives them a basis for talking about economics . . . .

"There was always an underlying feeling of unease about the future, contentment with the present and unease about the future. I think that the stock market crash ensures that that uneasiness won't go away and Democrats have something to work with in 1988."

Conservative political analyst Kevin Phillips predicted that "we are going to see a meaningful degree of shift" toward the Democratic Party on the basic polling question of which party does a better job handling the economy.

"When you look at the appeal of the Republican Party, what you are looking at is a great sense of confidence in Republican economic policy, having turned things around since '80 . . . . I think this {the market crisis} is going to put the Democrats ahead in more general economic management."

A Washington Post-ABC News Poll taken last June indicated that public opinion already was shifting to the Democrats. Asked which party was best equipped to handle the country's most serious problems, 47 percent of those surveyed said the Democrats, 41 percent said the Republicans. Asked specifically about the deficit, those surveyed said, by 50 percent to 40 percent, the Democrats were better equipped to reduce it.

Conservative political strategist Paul Weyrich said that the stock market is of particular importance "to the younger voter, the prosperity vote."

"If an adjustment occurs," he said, "I don't think it {the current market decline} is going to be that critical. If other consequences begin to flow, then I don't think that marriage {between the young and the GOP} is permanent."