Three years ago, there was an unexplained increase in the number of Russian intelligence officers operating in this country, according to administration and congressional sources.

The increase, which has not abated, reversed the almost 30 percent decline in the number of Russian operatives in the United States that had taken place after the 1991 breakup of the Soviet Union, the sources said. Much of the increase appears to be among Russian military intelligence officers who are engaged in economic espionage.

The number of Russian spies in the United States is speculative and closely guarded within the FBI. But sources said recently that when the Cold War ended there were roughly 140 officers of the Soviet KGB (the predecessor agency to Russia's SVR) and GRU (military intelligence) operating primarily out of the Soviet Embassy and military attache offices in Washington, Moscow's consulate in San Francisco, the Russian mission at the United Nations in New York, the U.N. staff and various trade missions.

That number dropped to roughly 120, sources said, when the Soviet Union broke up in 1991 and by 1995 was below 100, a counterintelligence source said recently.

During 1993 and 1994 the FBI shifted some of its personnel from covering Russian operatives to other targets, according to a government source. "It was the bureau's peace dividend," the source said. "Then the number started moving up again."

When the number of Russian spies began to increase three years ago, the CIA and FBI had talks with their Russian counterparts--a method of dealing with problems that has been employed quietly for years, and often with success.

But by 1997, when the so-called service-to-service talks showed no results, the Clinton administration began using diplomatic channels as well to persuade Russia to reduce its spies.

Russia's intelligence agencies traditionally have operated outside the purview of Moscow's diplomats and frequently without informing even top officials who work for the country's leaders. By questioning the increase in intelligence operations during high-level, bilateral diplomatic discussions, "we are demanding that the issue be looked at by people outside the Russian intelligence community. . . . We are telling them this has implications for our relationship," said an official involved in the process.

During arms control talks in the 1970s, Soviet foreign ministry negotiators, ignorant of what their military was doing in nuclear weapons, learned from the U.S. team about their own country's armament. U.S. officials again are trying to educate Russian diplomats and political leaders about the activities of their intelligence services, which normally operate without external oversight.

That was why Vice President Gore raised the issue last July when he met with then-Russian Prime Minister Sergei Stepashin in Washington.

At a news conference, Gore was asked about a report in the Washington Times that the United States was demanding a reduction in Russian spies. He responded: "We don't have to answer all the questions."

But Stepashin, who had helped direct the Russian equivalent of the FBI, then said there was "an agreement between the special services of Russia and the United States" to work "properly and adequately" on "a number of positions"--a reference to collaborations in the fields of terrorism, drug interdiction and organized crime.

Stepashin also made clear that the intelligence services would not be allowed to "hinder" relations between the two countries.

Gore added that although the Cold War had ended, tensions remained because "old attitudes in both countries fade away slowly." Without being specific, Gore said "sometimes agencies want to use old attitudes as an excuse for old budgets and old personnel rosters. And then the other side has to spend the same amount."

What has concerned U.S. officials is that much of the increased spying activity comes from officers of the GRU.

"They are more aggressive," said one experienced former counterintelligence official, "and have shifted into economic espionage, particularly in the civilian research and development area." Another intelligence specialist said the military attaches assigned here are the GRU's "best men because being here is better than being at home" in Russia.

Identifying Russian intelligence officers among that country's personnel here "is not a hard thing," said one former senior CIA official. Names come from Russian defectors who are always asked to identify intelligence officers with whom they have worked or trained and are asked to pick intelligence officers from rosters of personnel at the Russian Embassy and other Russian agencies in this country.

U.S. spies in Russia and the former Warsaw Pact countries also pick out Russian spies here.In addition, there are certain Russian Embassy and U.N. slots that traditionally are held by intelligence personnel.

After the breakup of the Soviet Union, the new Russian government said it would reduce officers from the GRU and the SVR. That same message was passed through the increasingly open back channel that ran between Russian and U.S. intelligence agencies and has existed in secrecy for 20 years.