In their time, the eight men had wielded power perhaps second only to that of the president. Some had stayed almost invisible. Others were thought to be imperial.

This weekend, top staff members for every president from Dwight D. Eisenhower to Ronald Reagan got together for the first time and found that they agreed far more on the tricks of their trade than their contrasting personalities and political philosophies made plausible.

At a 25th-anniversary convocation of the University of California-San Diego, taped for later broadcast on public television, eight men very familiar with the Oval Office aired their views on what makes the White House work.

The center of attention was H.R. (Bob) Haldeman, the ousted chief of staff under Richard M. Nixon. Haldeman, convicted in the cover-up of the Watergate break-in, insisted that Watergate would have been over "within weeks" and without severe damage "except that we didn't use our own staff system to handle it."

The others in the semicircle also cast long shadows across the Washington of their days: Haldeman's successor, Alexander M. Haig Jr.; Donald H. Rumsfeld and Dick Cheney, who divided the chief-of-staff duties under Gerald R. Ford; Jack H. Watson Jr., who moved into that job in 1979 when Jimmy Carter belatedly conceded that he needed such help; Andrew J. Goodpaster, Eisenhower's staff secretary; Theodore C. Sorensen, John F. Kennedy's wordsmith and special counsel, and Harry C. McPherson Jr., who served the same functions for Lyndon B. Johnson.

As fascinated scholars of the presidency listened to what they called the first such conversation among so many senior White House aides, the old staffers expressed some discomfort with all the publicity received by their current counterpart, Donald T. Regan.

"There's a difference between power and visibility," Watson said, noting that he and his predecessors were far less prominent on television than Regan has been.

"The chief of staff," Haldeman agreed, "has a vital internal role but not as spokesman or policy-maker."

Goodpaster said, "I find it hard to see how a chief of staff can be both strong and substantive" across the entire range of domestic and foreign issues.

But Rumsfeld, McPherson, Haig and Sorensen argued that the only judge of a White House staffer's worth is the president, and, as Rumsfeld put it, "This president likes him fine."

Rumsfeld, a 1988 Republican presidential hopeful, was implicitly critical of President Reagan for permitting a rapid turnover in recent years among national security affairs advisers. "Four . . . in five years," he exclaimed. "That's not good for the country . . . . The president should be held accountable, hell, yes."

Cheney, Wyoming's representative in Congress since 1978, said Regan was being unfairly criticized for involvement in the firing of Margaret M. Heckler from the Cabinet. "If there's a dirty deed to be done," he said, "the chief of staff has to do it." Cheney said that, in retrospect, "there are people I wish I'd fired" from the Ford administration.

While agreeing that the staff must be tuned to its boss' style, the eight veterans agreed that someone must be in charge.

Ford tried to give equal access and status to several aides, Rumsfeld recalled, calling them "spokes of his wheel." That did not work, he said, because in that arrangement, "the president becomes the grease . . . gets overheated and has to be replaced."

Carter started with the same notion, Watson said, and "it turned out to be a fatal mistake . . . . It pulls the president into too many issues. It means there's no cohesion." Haldeman said he ran "a tight ship" in his day but insisted that it was not designed to insulate Nixon but only to see that information reached him "in an orderly way." "I think we established a superb staff management system, much of which survives today," Haldeman said. "It worked superbly well for almost four years. I just wish we had kept it intact through our greatest crisis . . . . The system was not followed as Watergate went from a third-rate burglary to what it became. If it had been followed, we would have resolved that crisis in a few weeks . . . . "

At various points, almost all of the panelists denied that they exercised great power or influence over their presidents, but moderator John Chancellor of NBC News induced them to admit that they had ways of getting a president to give up "a damn fool idea."

"You do it very gingerly, if your president is Lyndon Johnson," McPherson said, drawing understanding laughs from the others.

Rumsfeld and Cheney said Ford was prone to give snap approval to what Cheney called "Oh-by-the-way ideas" slipped into conversation as calculated asides by scheming Cabinet members. The best way to stop these proposals was to "put them into the staff system," Rumsfeld said. "Sometimes, it took very long" for them to reappear, he added.

Sorensen said he used the same slowdown technique with Kennedy but also had a "short way to stop bad ideas. I'd say, 'That sounds like something Dick Nixon would have suggested.' " Haldeman and Haig joined in the laughter, and Haldeman had a topper when he noted, "Al and I didn't have the option to say what Ted did."

Failing that, Haldeman said he sometimes just ignored Nixon's orders, including one to "administer lie-detector tests to the entire State Department" to halt leaks that had irritated the president.

After stalling Nixon for a time, Haldeman said he finally admitted "I don't intend to" do that. To his relief, he said, Nixon replied, "I didn't think you'd do it."

Haldeman, now a Los Angeles businessman, has remained largely out of public forums since serving an 18-month sentence for his part in the Watergate cover-up. He clearly welcomed the opportunity to talk shop with counterparts in other administrations.

In a spirit of growing camaraderie, the others endorsed his arguments for a White House run through a strong chief of staff. Sorensen attributed the atmosphere to the fact that "we are all professionals dedicated to making government work."

At times, several of them said, that required them to become antagonists to others high in their administrations. Cheney acknowledged, for example, that as Ford's chief of staff, he developed a relationship of such "total hostility" with Vice President Nelson A. Rockefeller that Rockefeller told Ford that "the only way he would serve in a second term was if he could be chief of staff himself."

In response to questions, the eight unanimously opposed the recurrent suggestion that senior presidential aides be subject to Senate confirmation, as are Cabinet and agency heads. Except for Watson, all criticized proposals for changing the president's term to a single six-year tour.

They supported the usefulness of designating a national security affairs adviser, but their comments strongly suggested that this official should be less visible and influential than recent ones have been.

Sorensen expressed the consensus when he said that adviser "shouldn't make policy as much as Henry Kissinger did, shouldn't announce policy as much as Zbigniew Brzezinski did and shouldn't carry out policy as officers of the current National Security Council are doing in Nicaragua."