Rep. Jack Kemp (R-N.Y.) was at the University of Minnesota campus in Duluth last week campaigning for Sen. Rudy Boschwitz (R-Minn.), GOP House candidate Dave Rued, supply-side economics -- and himself.

"The only thing Walter Mondale and the Democrats have to offer is fear itself," he said, paraphrasing Franklin D. Roosevelt. "Fear of the future. Fear of the budget deficit in 1989."

In New Haven, Conn., Sen. Edward M. Kennedy (D-Mass.) arrived in a motorcade with a police escort and Secret Service protection to campaign for Rep. Bruce A. Morrison (D-Conn.) and the rest of the local Democratic ticket.

"Bruce Morrison will protect Social Security and Medicaid and is for nuclear arms control," Kennedy shouted to a partisan crowd. "Ronald Reagan is for mansions for missiles, slums for soldiers and is just asking voters to remember what their country has done for them."

In Trenton, N.J., last Thursday, Republican Gov. Thomas Kean told those at a party gathering that they were "lucky to have two people in the state who might be on the national ticket in the future -- maybe on it together!" He gestured toward Sen. Robert J. Dole (R-Kan.) and his wife, Transportation Secretary Elizabeth Hanford Dole, who were there on behalf of Mary V. Mochary, the GOP Senate candidate, and Rep. Christopher H. Smith.

"You'll see a lot of me in 1988," Sen. Dole joked. "I'll be carrying Elizabeth's luggage."

These are a few of the players in what promises to be a wide-open battle for the presidential nominations of both parties over the next four years, beginning Wednesday, the day after Election Day. Actually, for some it began years ago.

The Republican list of hopefuls to succeed President Reagan is headed by four familiar names -- Vice President Bush, Dole, Kemp and Senate Majority Leader Howard H. Baker Jr. (R-Tenn.). Other likely candidates are Delaware Gov. Pierre S. du Pont IV and New York businessman Lewis Lehrman, who ran unsuccessfully for governor of New York in 1982.

Most Republicans also will keep an eye on Sen. Jesse Helms (R-N.C.) if he wins his reelection bid.

The roster of possible Democratic successors to the Carter-Mondale period, assuming that Mondale loses today, is headed by Sen. Gary Hart (D-Colo.), who made a close race for the 1984 nomination; New York Gov. Mario M. Cuomo, the keynote speaker at this year's Democratic National Convention; Kennedy, about whom Democrats are divided between those who know he will run and those who know he won't; and Jesse L. Jackson, who also ran this year and is expected to try again.

Sen. Joseph R. Biden Jr. (D-Del.) appears set to go, some Democrats are beginning to talk up Sen. Sam Nunn (D-Ga.), and others mentioned include Sen. Bill Bradley (D-N.J.) and Govs. Robert Graham of Florida, Charles S. Robb of Virginia and Bruce Babbitt of Arizona.

The nomination fights in both parties will be waged to some extent along generational lines.

As in 1984, Democrats can expect a choice between such traditional New Deal-Great Society liberals as Kennedy and Cuomo and post-New Deal challengers such as Hart, Biden and Bradley.

Republicans will be asked to choose between such aggressive advocates of supply-side economics as Kemp and Lehrman, who are newcomers to the national scene, and more traditional budget-balancers and insiders like Dole and Baker.

"The secret to the Republican nomination is to control the Right but not be controlled by them the way Reagan has," one Republican campaign consultant said. "The way Mondale hasn't. Bush may be our Mondale."

The good news about Bush is that, as vice president, he is assumed to have an inside track on 1988, gets credit for a good showing in his nationally televised debate with Rep. Geraldine A. Ferraro (D-N.Y.), the Democratic vice-presidential nominee, and has shown exemplary vice-presidential loyalty to his president. The bad news is that many think he is too much of a cheerleader for Reagan and has been damaged by the "Doonesbury" cartoon joke that "he has put his manhood in a blind trust."

"His slavish devotion to the president has corrected the misapprehension of Republican moderates that he's one of them, but because of his tailoring and birthplace he hasn't won the loyalty of the Sun Belt conservatives," said John Deardourff, a Republican campaign consultant. "As a result, he's in sort of an ideological no man's land. He's also in danger of being Mondalized -- his fortunes are tied to those of the second Reagan administration and there's a danger that things won't go that well."

Kemp convinced many that he is a national-level player with his influence on drafting of the GOP platform in Dallas.

"I think he's the one to beat," one observer said. "No one has worked harder with the delegates and state chairmen."

He also is accumulating political IOUs by campaigning for other GOP candidates -- he has appeared on behalf of nearly 100 this year and his political action committee has contributed about $220,000 to them -- but he refuses to talk about 1988 while the 1984 election is under way.

Sources close to him, however, say that he'll begin moving around the country next year to line up support in key states and start traveling abroad to develop foreign-policy expertise.

"He's got a national media base and a hard-core network around the country," a Republican professional said. "But he can't play Hamlet. He has to go early and all out."

In Washington, Kemp is known as one of the most ardent exponents of supply-side economics, something of a Johnny One-Note on the subject. He says he believes that increased tax revenues from economic growth is the cure for the huge federal budget deficits and opposes any idea of "imposing any kind of a tax increase on this fragile economic recovery."

New Right groups credit him with supporting them on social issues such as abortion and school prayer, but he tries to relate such issues to economic ones.

"The impact of inflation and unemployment on the family is a social issue," Kemp has said. "We ought to double the tax exemption for children. It used to be socially desirable in this country to have children."

Dole, chairman of the tax-writing Senate Finance Committee, is on the other side of the tax issue from Kemp. Unlike Kemp, he says budget deficits endanger the economic recovery and can be dealt with best by freezing federal spending levels and raising taxes "in the last resort."

"Freeze spending, except for a 5-percent growth for defense and some for programs for the elderly, and you get $50 billion out of the deficit just with that," he said. "The idea that you can eliminate it with growth sounds great because it's painless. I don't see how we can do it, however."

Dole has campaigned on behalf of about 60 Republicans in 20 states and has contributed about $1.1 million to GOP candidates. He's vague about his intentions, however.

"If the economy is strong, '88 would be a good year but I've got a reelection race in '86 and I'm taking a look at the majority leader position," he said last week.

Baker is retiring from the Senate and Dole is a favorite to succeed him as majority leader. One reason Baker gave for ending his 18-year Senate career was his conviction stemming from his unsuccessful 1980 presidential race that running for president is a full-time job.

"We'll look at '88 next year to see who will work with him, laying out strategy and start raising money," one senior adviser to Baker said last week. "We've got to find out if we can raise money and it's a daunting task.

"Mondale lasted this year because he raised money early and had a cushion against his setbacks. But look what it took: in 1983 I'm told that he made 213 fund-raising appearances, that's four a week before groups of 20 or 30 or 40, plus hundreds, maybe thousands, of phone calls."

Some GOP professionals see a hard role for Dole and Baker because they're Washington insiders who will wind up selling the need for a tax increase to lower the deficits. Some doubt that Baker has the fire to make the race.

"He got going too late in '80 and had to work with the fourth or fifth level of volunteers," said one.

"He had lots of money but no personal energy," said another. "He couldn't get himself organized to do anything."

Energy and money are not problems for Lehrman and du Pont, but neither man has a national reputation and Lehrman has never held public office. Both have traveled extensively around the country, du Pont with a political action committee that supports state legislators and a group that schedules him with young business leaders.

Lehrman has a national organization in 225 congressional districts and has traveled to more than 35 states. He spent about $7 million of his own money in 1982 in losing to Cuomo by 180,000 votes out of more than 5 million cast.

"There's no limit to what he can spend," one Republican consultant said. "His drug company stock went up so fast that year that he made it faster than he could spend it."

On the Democratic side, Hart is considered the early front-runner because of his experience, staff and fund-raising base.

"This can absorb a lot of difficulties but he carries a lot of baggage," one Democratic professional said last week. "He made a lot of mistakes this year and there's some question about his temperament."

Hart has been one of Mondale's most enthusiastic supporters this fall, which most interpret as a signal that he's a good Democrat and intends to run again. But he also has to make a decision on his Senate reelection race in 1986 and has a campaign debt of nearly $4 million, which means that every day until the end of the year -- while he is still eligible for matching funds -- will be devoted to fund-raising events.

"He'll try to get into legislation the industrial policy, job displacement training and hunger programs he talked about during the campaign this year," Kathy Bushkin, his press secretary, said. "He still has the same ideas and messages that drove him to run this year."

Some Democratic professionals say Kennedy is putting out signals that he's going to run next time, but some urge caution. In an interview in the Boston Herald recently, Kennedy said he wanted to be president but made no commitment to 1988.

"In a crowded field he has a hard base of 30 percent to 40 percent," one said. "But there is a strong view in the party that he couldn't win the general election because of the negatives on his personal character."

Professionals in both parties admire Cuomo's intelligence and eloquence.

"He's more attractive than anyone else in either party," one Republican said last week. "He has the capacity to excite people and I think he's impressed many by taking on the Roman Catholic Church the way he has" on the issue of abortion, in particular.

Cuomo has a reelection race in 1986 but has avoided locking himself to a full term.

"He doesn't think four year presidential campaigns are necessary," one adviser said. "But he has reservations about it. He's happy and comfortable being governor and is familiar with the state, its problems and issues."