The National Security Agency, the supersecret U.S. eavesdropping agency, has indicated to the organization of political extremist Lyndon H. LaRouche Jr. that it has conducted an investigation of the group. The agency has declined to elaborate about the probe, saying disclosure "could reasonably be expected to cause exceptionally grave damage to the national security."

The NSA revealed the investigation in a letter responding to a LaRouche group request for a search of NSA files under the Freedom of Information Act.

LaRouche group lawyers have indicated that they intend to request that the government research the matter to discover whether the files contain information relevant to the upcoming federal trial in Boston of LaRouche and 13 associates charged with credit card fraud and obstruction of justice. LaRouche associates also have alleged that the probe is part of an illegal investigation of the group, although they have provided no evidence.

Two months ago, LaRouche group attorney Bernard Fensterwald III of Arlington wrote to the NSA requesting documents in connection with any electronic surveillance of 11 LaRouche-related groups on national security grounds since December 1981. He also sought information on any investigation of the groups during that period in connection with terrorism, subversion and other areas.

On July 27, the NSA responded that it had files that fit those descriptions on only one of the groups, the Schiller Institute. In the agency's letter to the LaRouche organization, it said the files were classified top secret and declined to describe the probe for reasons of national security.

The Schiller Institute, one of many organizations in the LaRouche orbit, was founded in 1984 by his wife, Helga Zepp-LaRouche, a West German citizen. Most the Schiller group's activities are centered in Europe, especially in Wiesbaden, West Germany, where the LaRouche group has offices.

The organization, named for 18th century classical German poet Friedrich Schiller, holds conferences and distributes literature espousing the conspiracy-minded LaRouche line, and generally is anti-Soviet and in favor of NATO nations strengthening their militaries.

John Markham, the assistant U.S. attorney leading the LaRouche prosecution, declined to comment on the NSA letter.

In addition, the FBI responded cryptically to the LaRouche organization in a way that suggested it also had files about the Schiller Institute. The group had sent an identical Freedom of Information request to the FBI, requesting information on all 11 groups.

The FBI responded in a letter on July 30 that made no mention of the other groups, but said that releasing information about the Schiller Institute is barred under a 1979 federal court order in New York. That order -- stemming from a long-running lawsuit that LaRouche and some associates filed against the bureau -- limits the FBI's release of information about the LaRouche group.

Last week, top LaRouche aide Paul Goldstein filed suit in federal court in the District against the NSA, FBI, CIA and nine other federal agencies, demanding release of files on the organization.

The NSA, whose operations are secret, monitors some overseas telephone calls and other communications from listening posts around the world.

The LaRouche group, which has alleged for years that it is the target of illegal government investigations, trumpeted news of the NSA revelation. It said in a news release last week that it believed the FBI asked the NSA to listen to the group's communications as part of a counterintelligence investigation. FBI counterintelligence investigations focus on possible spying or other activities for a foreign power.

While the FBI has led a 22-month federal investigation of the LaRouche group, the bureau has not acknowledged any recent interest in it on counterintelligence grounds. But the FBI did investigate the group for possible ties to at least one foreign government in the early 1970s, when LaRouche was a Marxist. Later he turned the group to the far right, and now its politics are a mixture.

The LaRouche group, while acknowledging that its associates have kept in contact with Soviet bloc officials, has said it never has engaged in espionage.

A number of U.S. intelligence specialists have raised the question of whether the group's turn to the right was a ruse and whether it acts as a stalking horse for the Soviet bloc.

In a Jan. 12, 1982, memo, then-FBI Director William H. Webster said that numerous members of the President's Foreign Intelligence Advisory Board had "raised the question of the {group's} sources of funding" out of fear that it "might be funded by hostile intelligence agencies."