Baggy eyes and a banged-up knee, Amy Carter and a faulty audio system - each has played a part in the brief history of televised presidential debates and helped determine the course of history.

When George Bush and Michael Dukakis step onto the stage in Winston-Salem, N.C., Sunday evening, it will be only the 11th time in 200 years that the two major-party nominees have come together to argue their rival claims to the White House.Television debates are a recent phenomenon, dating back merely to 1960. But already they have become such an institution that no future candidate can avoid them.

"These joint appearances deserve to be made a permanent and integral part of the presidential election process," said Paul Kirk and Frank Fahrenkopf, chairmen of the Democratic and Republican national committees, in a joint statement in 1985.

That doesn't mean that every nominee is eager to debate. Often it's quite the opposite. In their brief life, debates have become the most crucial, high-risk events in a presidential campaign. A trap question, a careless answer or even bad lighting and makeup can be devastating.

In fact, a well-placed Bush campaign aide, who asked not to be identified, said the vice president would have preferred not to debate the Massachusetts governor at all this year. Dukakis had wanted four debates; Bush reluctantly settled for two.

Usually, the underdog or lesser known candidate craves debates, while the front runner or incumbent president prefers to dodge them. In 1940, for example, Wendell Willkie, the Republican nominee, challenged President Franklin D. Roosevelt to debate; Roosevelt ignored him.

In 1960, however, there was no incumbent, and the two candidates, Richard Nixon and John F. Kennedy, each accepted the television networks' invitation to debate.

Newton Minow, a Kennedy adviser, said the Democratic nominee thought the TV exposure would help him "overcome two of the biggest obstacles to the presidency - the perception that he was young and inexperienced, and the possibility of an irrational reaction to his religion."

Nixon had triumphed in debates in his first Senate campaign, and his famous 1952 "Checkers" speech had convinced him he knew how to use television to his own benefit, Minow said.

Faulty makeup and a knee injury put Nixon at a disadvantage in the first of four debates. He never recovered.

More than 100 million Americans watched at least part of the 1960 debates, and a CBS pollster found that 57 percent of those who voted said they were influenced by the debates. By one estimate, Kennedy owed 2 million votes to the debates, far more than his margin of victory of only 112,000 votes.

President Lyndon Johnson refused to debate Barry Goldwater in 1964, and Nixon, far ahead in the polls, rejected debates with Hubert Humphrey in 1968 and with George McGovern in 1972.

The encounters resumed in 1976, when President Gerald Ford trailed Jimmy Carter, then a little-known governor, by 30 points in the polls. Ford and Carter met three times, and the first vice presidential debate, between Robert Dole and Walter Mondale, also took place that year.

The 1976 debates were marred by an audio failure during the first Ford-Carter debate. The candidates stood at their podiums like a pair of wooden Indians for 27 minutes while technicians frantically struggled to fix the equipment.

More important, Ford said that Poland and other Eastern European nations were not under Soviet domination, stirring a storm of protest and ridicule. And Dole's harsh comment that 1.6 million Americans died in "Democrat wars" backfired against him.

In 1980, it was Carter's turn to be ridiculed for dragging his 10-year-old daughter, Amy, into his only debate with Ronald Reagan. "I had a discussion with my daughter, Amy, the other day, before I came here, to ask her what the most important issue was," the president said, while his staff groaned. "She thought nuclear weaponry - and the control of nuclear arms."

"I lost the debate . . . and that hurt badly," Carter was later quoted as saying.

By 1984, debates had become institutionalized, and Reagan, even though he was the incumbent and far ahead of Mondale, agreed to two meetings.

Reagan's lead was so overwhelming it was doubtful the debates could make a difference. Nevertheless, they offered Mondale his best chance, and for a brief time it seemed to work. Reagan, tired and over-coached, flubbed the first debate. His own pollster, Richard Wirthlin, saw his lead slip from 19 to 12 points in the first four days.

But Reagan recovered in the second debate, when Mondale looked pale and baggy-eyed, and the president rolled on to his November landslide.