To paraphrase a famous question from an earlier congressional investigation: what did Henry Kissinger know, and when did he know it?

That query, representing a major uncharted area of the Korean influence-buying scandal, will come to the fore Wednesday when a House subcommittee begins public hearings designed to determine how much Kissinger and other Nixon administration officials knew about the street South Korean effort to win friends through bribery in Congress.

People who have seen the subcommittee's evidence claim the hearings will make a compelling case that the administration knew about the illegal activities of secret Korean agents in Washington but did nothing to warn members of Congress who had contacts with those agents.

To try to establish that, Chairman Donald M. Fraser (D-Minn.) of the House International organizations subcommittee will take testimony this week from witnesses who held key positions in the State Department, the FBI and the intelligence agencies during the Nixon era.

Lawyers on the Fraser subcommittee staff admit that their evidence leaves room for several explanations - ranging from "deliberate cover-up" to simple negligence - for the executive branch's failure to warn Congress.

But the staffers said their hearings would leave "no doubt whatsoever" that the State Department, the Justice Department and the intelligence agencies knew of the Korean scheme in the late 1960s and early '70s.

The subcommittee plans to release documentary evidence that includes confidential messages from intelligence agents warning of the secret Korean program. Kissinger and former attorney general John N. Mitchell were on the distribution list of these messages, staffers say.

The subcommittee staff spent much of last week in intensive negotiations with Kissinger trying to convince him to testify. But a Kissinger spokesman said that the former secretary of state, who was invited, but not subpoenaed, to appear, had not yet decided if he will.

The subcommittee also invited Mitchell to testify. A committee lawyer said Mitchell's appearance is uncertain because of concern for his health.

Since the first public reports that the South Korean government had used agents here to buy influence in Congress, it has been suggested that the Nixon administration knew about the effort but kept mum.

Sen. Lowell P. Weicker Jr. (R-Conn.), a member of a Senate committee probing the Korean affair, said recently that the administration was guilty of a "cover-up" in the case.

The hearings are scheduled for Wednesday and Thursday this week and the following Tuesday and Wednesday. In addition to probing the Nixon administration's knowledge of the influence-buying effort, the sessions will focus on two questions: why the South Korean government decided it had a problem in Congress in the late 1960s, and why it decided that bribery and party-giving were the best mtans to solve the problem.

The Fraser subcommittee's investigation of the Korean case is separate from the better-publicised investigation being pursued by Leon Jaworski for the House Committee on Standards of Official COnduct.

Fraser, who is giving up his House seat this year to run for the Senate, has chafed somewhat about the relative ignorance around the nation of his subcommittee's work while Jaworski's investigation is widely known.

While Fraser's subcommittee is pursuing its public Korean hearings, the Senate Ethics Committee is to begin private interrogation of Tongusn Park, the Korean rice dealer alleged to have been a central figure in the influence-buying scheme, to ask about his contacts with present and former senators. (SECTION) enate staff aides said they already have considerable detail about Park's activities on their side of the Capitol. On the basis of Park's earlier testimony to the Justice Department, they expect to major new developments to emerge.

But the sessions, scheduled for four days beginning Tuesday, will still be important, the Senate lawyers say. They will give Ethics Committee members a first-hand opportunity to determine how believable Park's testimony is.

If he appears to be a "reasonably reliable witness," the committee will move on the public hearings later this spring, according to Victor Kramer, the committee's special counsel.

Kramer, proffesor at Georgetown University Law School, said he is anxious to hold public hearings as quickly as possible because "the length of time it has taken to gather information in this case has cuased the American public to exaggerate the extent of involvement of present and former senators."

Last week Park concluded six days of secret testimony before the House Committee on Standards of Official Conduct, which is probing House members' involvement in the Korean case.

Although Park apparently implicated to member of Congress whose names had not come up previously, committee members and staff lawyers said the questioning did advance their case.

"The most important thing was that we pinned down, absolutely, the fact that Park was acting as an agent of the South Korean government," said a committee investigator, who asked not to be identified.

Park and the Korean embassy here have steadfastly denied any such connection, and Park reiterated that position after he finished talking to the House committee last week. But the investigator said the committee's evidence establishes "conclusively" that Park was a government agent when he distributed gifts and money on Capitol Hill.

That point is important to the House probers, because certain contacts between Park and members of Congress would be illegal if Park were shown to have been a foreign agent.

After a week-long public hearing this spring to review the entire Korean matter, the committee may hold a series of shorter hearings to deal with specific allegations of misconduct against individual members of Congress.

Committee investigators have been reluctant to estimate how many members might be subject to discipline. Recent estimates, all unverified, have put the number somewhere between two and 24.