Public revelations this week about a high government official who periodically beat his wife have brought to the fore an age-old Washington question -- when does a public servant's private behavior affect his ability to keep his job?

John M. Fedders, chief enforcement officer at the Securities and Exchange Commission, resigned Tuesday after admitting that he beat his wife during their 18-year marriage. He was not charged with a crime, and there was no indication that his personal problems hurt his performance at work.

Is this a clear-cut case in which a public official should be forced from office? And exactly when should a public official's personal life become grounds for firing -- or for a news story? These are questions that have perplexed politicians, academics, lawyers and journalists for years.

"We are really uncertain about the whole area of the private in American life," said Bruce Payne, a professor of ethics and public policy at Duke University. "On the whole I think we ought to keep private lives of public people as private as is reasonably possible. But when they do things that by their standard and by the mass public's standard are deeply wrong, it may be inappropriate for them to remain in high position."

The revelations about Fedders' spouse abuse came to light in testimony from his wife Charlotte during the couple's divorce trial last month in Montgomery County Circuit Court. But months before, White House counsel Fred Fielding learned of the allegations against Fedders when a letter to President Reagan from Charlotte Fedders was delivered to the White House by her sister. Some staff members on Capitol Hill said they heard rumors of John Fedders' wife beating a year ago.

"Part of the hypocrisy is that we are willing to tolerate criminality, illegality and immorality unless it comes to the attention of a court," said Harvard Law School professor Alan Dershowitz. After news accounts of the beatings surfaced this week, the White House said no action would be taken against Fedders pending the outcome of his divorce trial, which has been postponed until May. A White House official said the administration did not want to interfere in a private matter that was being handled by the courts. But Fedders quickly stepped down.

Fedders' marital problems, his mounting debts and his role as an outside lawyer for Southland Corp. during a time when the company was accused of covering up a bribery scheme were first reported on Monday in a front-page article in the Wall Street Journal and the next day in The Washington Post and other newspapers.

"This was obviously a very agonizing decision for us," said Stewart Pinkerton, an assistant managing editor at the Journal. "Generally we don't think we ought to be writing about public officials' private lives when there is no indication that whatever is going on is affecting their performance of their public duties. But when you added everything up about Fedders , there were fairly compelling arguments for writing about this."

Washington Post Executive Editor Benjamin C. Bradlee said the Fedders case was clear-cut.

"Moral turpitude on the part of someone involved in law enforcement is a pretty good definition of news," Bradlee said. "You can't do your job while you're breaking the law. Your hands aren't clean."

Ethics experts, media critics and government officials interviewed this week seem to agree there are three clear cases when a public servant's personal conduct is newsworthy and warrants firing: First, if there is substantiated evidence that an official has committed a serious criminal or moral offense; second, if the official's conduct has impaired his ability to perform his duties, and third, if the official abuses his office.

The rules can get blurry when an official's conduct is questionable but he has not been charged with a crime. "There is a set of ethics you have to subscribe to if you're going to buy into the high levels of Washington," said Don Wortman, acting director of the National Institute of Public Affairs. "The public has every right to demand an extremely high standard. If you are a known wife beater, you have ruined your political effectiveness."

"The higher . . . the governmental position held, the stricter the ethical standard should be," said Sen. Joseph R. Biden Jr. (D-Del.), who questioned Attorney General Edwin Meese III's ethics during Meese's confirmation hearings last month.

A special prosecutor had investigated allegations that Meese, while serving as counselor to the president, arranged federal jobs for friends who had given him loans. The special prosecutor concluded that Meese had done nothing illegal. But Biden argued that an attorney general should be held to a higher standard than simply obeying the law.

Some, including Biden, said appearances of personal or professional misconduct can become grounds for dismissal. When accusations first arose that President Carter's chief of staff, Hamilton Jordan, had snorted cocaine, Jordan wanted to resign, according to Lloyd Cutler, White House counsel at the time.

"We had to prevent him from resigning . . . . He wanted to resign although he was perfectly innocent," Cutler said. "I'm quite sure if we had known of a continuing drug user on the White House staff we would have removed him."

Said Hodding Carter, a media critic, former newspaper editor and Carter administration official: "In any public position you should follow the old cliche, 'Public office is a public trust, not a public right.' When you go into public life you better damn well understand . . . it's got to be a glass house."

As the Fedders case demonstrated, the media are closely intertwined with public officialdom when it comes to judging the private lives of public servants. Often, publicity about an official's personal problems is what ultimately forces him from office.

Typically, the media have steered away from reporting about the personal lives of members of Congress or high-ranking administration officials in cases where extramarital activities, homosexual relationships or alcoholism are known.

Rep. Wilbur D. Mills (D-Ark.) lost the chairmanship of the House Ways and Means Committee in 1974 after a nighttime companion, stripper Fanne Foxe, jumped into the Tidal Basin at 2 a.m. as Mills looked on. Prior to the episode, the media had indications that the congressman was a heavy drinker and that drinking at times had interfered with his work. In the aftermath of the scandal, Mills conceded that he was an alcoholic, but the media had not reported on his drinking problem until then.

Rep. Wayne L. Hays (D-Ohio) resigned in 1976 after disclosures that the newly married congressman had had a mistress, Elizabeth Ray, on his congressional payroll.

Voters removed Rep. Robert A. Bauman (R-Md.) from office in 1980, months after he was arrested for soliciting sex from a teen-age boy. But Rep. Gerry E. Studds (D-Mass.) won reelection last year despite being censured by the House for a homosexual relationship with a teen-age page.

This week, Judge Albert B. Fletcher Jr., who sits on the nation's highest military court, was convicted in Fairfax County of soliciting sodomy from an undercover policeman. The president and Congress have the power to remove him from the bench, but White House spokesman Larry Speakes said Reagan has no plans to ask for his removal.

On the whole, there are few instances in which revelations of personal problems rather than professional improprieties have ended careers. Now, however, the pendulum may be swinging in the opposite direction, according to Columbia School of Journalism professor emeritus Fred W. Friendly and other media critics. This is partly because mores have changed. For example, they said, the media gave little attention 30 years ago to problems such as domestic violence, alcoholism and drug abuse. Today those issues cause widespread public concern.

Some critics worry that the media have gone overboard. "There is too much emphasis on the private lives of public officials when there is no direct evidence that their behavior seriously affects their public performance," said Ben Bagdikian, a journalism professor at the University of California. "It's a misplacement of priorities in judging public figures."