President Reagan begins his second term in office with a historic opportunity to capitalize on his landslide reelection and turn the Republicans into a majority party that could dominate American politics for decades.

Republican fortunes appear as bright as at virtually any time since they lost their dominance to Franklin D. Roosevelt and the New Deal coalition. Republicans have achieved, at least temporarily, rough parity with Democrats in party identification and seized the initiative as the party of change. In other critical measures, voters now see Republicans as the political organization best able to solve problems facing the country.

Much of this is clearly due to Reagan -- his personality and style and the conservative ideology that has guided him since he emerged on the political scene during Arizona Sen. Barry Goldwater's 1964 presidential campaign. But there is more to it than a popular president. Several economic and social forces have combined to help Republicans.

Yet the Republicans' future remains uncertain for various reasons that even Reagan may not be able to influence.

Most important is that Reagan's bold economic experiment is not yet a certifiable success. Any downturn in the economy in the next few years could undermine Republicans' hopes of becoming the majority party.

There are also deep divisions within the party and the coalition it seeks to build. Reagan has managed to control these differences, but whether the party can survive his departure from the political scene is a troubling and unanswerable question for many Republicans.

Finally, though the Democratic Party remains divided and uncertain about how to move forward, the existence of many bright and attractive young Democratic leaders gives hope to Reagan's opponents that their time in the wilderness may be only temporary.

Many Democrats initially dismissed Reagan's 49-state victory over Walter F. Mondale last November as little more than a personal one. They pointed to the Democrats' gain of two Senate seats and the loss of just 14 House seats, with one still undecided, as evidence that the emperor had no coattails.

Post-election analysis suggests otherwise.

"My feeling is that the days of one-party advantage are really over," said Peter D. Hart, Mondale's pollster last year. "We're in a competitive two-party system."

Richard B. Wirthlin, Reagan's pollster, was even more emphatic, saying: "Partisan politics had been static in America for a long time. The Democratic dominance was challenged but not shattered in 1980. In 1984, that dominance disappeared."

Even Rep. Tony Coelho (D-Calif.), who as chairman of the Democratic Congressional Campaign Committee helped prevent more substantial losses in House races, said his party has achieved minority status at the presidential level. "As far as the federal government is concerned, we're the minority party," he said. "Out in the country, at the state and local level, we're the majority party."

Changes in party identification were perhaps the most significant and surprising political development during 1984. Election Day exit polls and post-election surveys confirm that Republicans have reached near-parity with Democrats.

The high-water mark for Republicans came in a post-election poll by Robert Teeter of Market Opinion Research for the National Republican Congressional Committee. He found that 47 percent of respondents nationally said they were Republicans or leaned that way, compared with 41 percent who called themselves Democrats or Democratic leaners.

"There's probably some [election] afterglow, but we've gone from a period when we've had a big [difference in party identification] to a position where we're not going to be very far away from parity," Teeter said. "The plan is to go on from there to be a plurality party. I don't think we're there. But the Republicans made huge progress."

Other polls, while less dramatic, also indicated an important shift this year.

The CBS News/New York Times exit poll on Election Day measured party identification two ways, finding in one that 32 percent of voters called themselves Republicans, 32 percent Democrats and 36 percent Independents. When so-called "leaners" were allocated, results showed Republicans with a 47-to-44 edge, with 9 percent calling themselves Independents.

Changes in key states reflect changing dynamics in the country. ABC News exit polls showed Republicans with a 35-to-33 percent edge in party identification in Texas, historically a strongly Democatic state.

In Florida, where Democrats have enjoyed a wide registration edge, Republicans trailed Democrats, 39 to 37 percent. In Illinois, the two parties were virtually even. In California and New York, the Democratic edge was larger but shrinking -- 6 points in California and 11 in New York.

Hart reportedly rattled Democratic senators in December when he told them what happened in Alabama among white voters last year. In December 1983, 53 percent called themselves Democats, 29 percent Republicans. By Election Day, 41 percent said they were Republicans and just 24 percent Democrats, a shift of 41 points in fewer than 12 months.

"It was in the South more than anywhere else," Hart said, "but you saw it everywhere."

Republicans were disappointed by their relatively modest House gains in November. House Minority Leader Robert H. Michel (R-Ill.) said the day after the election that the party should have done much better and blamed Reagan and his campaign team for failing to help congressional candidates enough.

But Republican strategists have since taken heart from post-election studies of votes in House races. Overall, Democrats led Republicans by 52 to 48 percent, a narrower difference than in past years. But in contested House races, Democrats received 49.6 percent to 49.3 percent for Republicans. The GOP failed to contest about 50 House seats.

Furthermore, asked in a poll by Democratic pollster Patrick Caddell how they intended to vote in future House races, respondents chose the Democratic Party by just 44 to 43 percent.

As a result, Republicans blame the Democrats' 252-to-182 House majority on what they call gerrymandered congressional district boundaries and have targeted 1990 state legislative elections as the key to winning the House in the next decade.

No one underestimates Reagan's importance in Republican Party advances. "That's like asking what role Dan Marino or Joe Montana played in getting the Miami Dolphins and the San Francisco 49ers to the Super Bowl," Rep. Jack Kemp (R-N.Y.) said, borrowing a metaphor from his past as a professional football quarterback.

Even Reagan's former adversaries say the Republicans' advances could not have happened without him.

Rep. Dick Cheney (R-Wyo.), who was White House chief of staff under President Gerald R. Ford and was in the middle of the 1976 nomination fight between Ford and Reagan, was asked whether Republicans would be where they are today if Ford had defeated Jimmy Carter in 1976.

"I'd have to say honestly, probably not," he replied. "That's not a criticism of Gerald Ford. But two things were critical to our success. One is Ronald Reagan. The other is Jimmy Carter. You sort of had to have Carter to have Reagan happen."

During last fall's campaign, Vice President Bush's wife, Barbara, was asked by Washington Post staff writer Dale Russakoff whether her husband, had he won the presidency in 1980, could have ushered in the kind of patriotic, upbeat mood that exists in the country.

"Probably not, to be absolutely honest," she responded. "And I bet George would tell you the same thing . . . . I don't know whether it's because George was so close in -- he'd been in Congress, and he'd been in government. But I can't think of one other person in America who could have gone up to the Hill and had the response [Reagan] did in the first two years."

Several things about Reagan have contributed to Republicans' success.

The first is his ideology, changed little in his two decades in politics. "Ronald Reagan's message has not changed in 20 years," Wirthlin said. "But the mood of the public has come into closer and closer congruence with what people think government should and should not do."

Caddell said his firm did extensive interviewing last summer to determine keys to Reagan's success. "He's not the omnipotent, beloved person people in Washington think he is," Caddell said. "Ronald Reagan's strength is that he's an ideologue. He does believe in something. He believes in what he says at a time when no one thinks any politician believes in anything."

If convictions and ideology are essential, so is Reagan's personality. "What he's been able to do [as president] is a continuation of what he's done for a generation," Hart said. "He made the message of conservatism palatable to listen to in 1964. He's made the Republicans a lot more acceptable, something that people will listen to. And he did it against the perception that his administration is unfair."

Cheney said another key is the appearance of success. "Ronald Reagan appears to have a competent government that works," he said.

Republicans also have benefited from Reagan's ability to communicate a sense of strength, hope and optimism about the nation's future, according to several Republicans and Democrats, in contrast with a more confusing Democratic vision. In that sense, Reagan's and the Republicans' progress is intimately linked to Democrats' problems.

"I think the country was ready for Reagan, and Reagan was ready for the country," Senate Majority Leader Robert J. Dole (R-Kan.) said. "It was a perfect match."

Rep. Newt Gingrich (R-Ga.), one of the young Republican House leaders, said four factors converged under Reagan. He cited a shift in power nationally toward traditionally more conservative regions, the rise of the modern conservative movement, the "collapse of the welfare state as an intellectual concept" and Reagan's ability to communicate.

"His quarterbacking, his leadership, his ability to motivate were instrumental," Kemp said. "But I'd like to think he's had some good resources at his disposal to move our party to potential majority status."

Those resources include a breakdown among Democrats.

"The signs have been there all along," Hart said. "People have chosen to ignore them. What happened in 1984 wasn't the result of some awful miscalculation in 1983. The erosion has been there for 16 years."

Sen. Gary Hart (D-Colo.), whose unsuccessful presidential campaign last year helped to expose problems within his party, discounts Reagan's personal role in Republicans' increased popularity, noting that the president simply "capitalized on a period of transition in the Democratic Party."

Since the early 1970s, Hart said, "in terms of both themes and substance, and ideas, our party has been out of steam. I think we permitted a vacuum to form which Ronald Reagan has partly filled. I think the real question is what happens after Reagan."

Some Democrats argue that a crucial part of the answer is what the Democrats to do themselves in the meantime.

Caddell, a Hart adviser last year and previously pollster for Carter and former senator George McGovern (D-S.D.) in his 1972 presidential campaign, said the 1978 midterm election is the point at which the Republicans seized the initiative.

"The [Democratic] Party's great strength has been as an initiator," Caddell said. "Since 1978, we've been the party of the status quo ante . . . . So it's not Ronald Reagan per se. There are far more fundamental things at work."

By embracing supply-side economics, Reagan became the vehicle for "this intellectual surge of energy" inside the GOP, Caddell said.

"The Democratic challenge," Sen. Hart said, "is to recapture the initiative -- symbolically, thematically and substantively."

Republicans dreamed of becoming the majority party in early 1981, only to see their hopes dashed by the recession that began late that year. Those memories remain vivid -- Peter Hart predicts that the GOP will regress somewhat this year -- but some Republicans argue that the party begins this term of Reagan's presidency with several added advantages.

Foremost are 1984 election gains among new and younger voters and with certain groups within the electorate. Wirthlin said Reagan attracted 64 percent of voters age 24 and under, compared with about 44 percent in 1980.

"In 1981, the electorate flirted with the Republicans for three to four months but went back to their allegiances on Election Day," Wirthlin said. "I think this shift could be more permanent because of first-time voters."

But pollster Hart said he thought young voters were "terribly much up for grabs," adding, "They're the least solidified, have the fewest moorings."

The GOP also has benefited from the growing role of born-again Christians, has sunk its roots more deeply in the South and has shown that it can appeal to urban Roman Catholics and blue-collar workers.

"The trends keep going in the wrong direction among key voting groups," said William Hamilton, a Democratic pollster who worked for Sen. John Glenn (D-Ohio) in the presidential race.

Many politicians question whether Republicans can successfully and durably cement the coalition of traditional conservatives, business interests and the religious right, especially as Reagan fades from the scene.

"It's not a natural coalition they've put together," Hart said. "The struggle for power is going to cause certain fissures. But, if the Democratic battle plan is based on Republican internecine warfare, it's a bad plan."

What then lies ahead? "It depends on how much of a struggle we have the next four years for the soul of the party and what happens in the midterm elections," Dole said.

Politicians of both parties cite several crucial periods ahead, the first this year when Reagan tries to reduce federal budget deficits and make significant progress on an arms-control agreement with the Soviet Union. All sides agree that Republican fortunes hinge on continued economic growth. "If we have a depression, then we're back in the open as to which party dominates," Gingrich said.

Dole, calling Republicans the minority party, said a combination of policies is needed to help the GOP. "I think many of the skeptics and the doubters who might come to our party are concerned about arms control and whether Reagan's too much a defense advocate," he said. "On the economy, I think we went too far in 1981 and became the party of big deficits."

What role the lame-duck president plays in the debate this year may help determine the party's future, and some Republicans contend that he must be more aggressive than in 1981. "He's got to be willing to take on the Congress," one Republican said.

The fruits of 1985 are likely to affect next year's midterm elections, when Democrats hope to regain Senate control. After that comes the fight that many Republicans fear most -- the battle for Reagan's mantle.

Potential successors are aligning support for the 1988 race. They include Bush, Kemp, Dole and former Senate majority leader Howard H. Baker Jr. (R-Tenn.). "I don't assume it will break out until after the 1986 elections," Dole said. "I hope [Reagan] doesn't try to pick anyone to lead the party."

Sen. Hart said he believes that the succession struggle gives Democrats cause for optimism. "If I saw a young Ronald Reagan on their side, I'd be more worried," he said.

A fundamental realignment has not occurred, Hart said. "It could happen. The Democrats have four to eight years to prevent that from happening," he added.

Republican strategists said their party must do several things to keep moving forward.

"As long as the economy is growing to some extent over the next four years, you can gradually bring federal spending under control, you can gradually bring the deficit size under control," Gingrich said. "And, if you convince the public that the deficit is a function of spending and not taxes, I think conceivably you can sustain a political majority the whole rest of this century."

The two parties are dealing in speculation about a future they cannot predict. That the landscape has been changed, in large part because of Reagan, is unarguable.

But, as pollster Hart said of Republican advances, "How deep, how firm, how solid, I don't know . . . . The next four years are going to be terribly interesting. The climb up the mountain is a lot easier than staying at the summit."