MOSCOW -- In August 1984, President Reagan made an off-hand joke about bombing Russia. The remark, accidentally picked up by a microphone, reverberated loudly in the Soviet press, where it was seized upon as more proof that the United States was led by a madman bent on war.

Those were the days when Ronald Reagan was seen here as a Hollywood cowboy stuck in the "Procrustean bed of ossified anticommunism," a man whose speeches were "shameless lies from beginning to end" and whose imperialist policies were likened to Hitler's.

For average Soviets, the bombing joke was troubling: either it meant Reagan really was as aggressively hostile to the Soviet Union as Soviet propaganda had been saying, or it meant that the U.S. president was a fool. Neither thought was very comforting to Soviets or flattering to Reagan.

But during the past few years, as U.S.-Soviet relations improved, that image has faded almost completely. Judging from recent conversations with Soviet citizens, Reagan, in the popular mind, has now become a neutral figure -- an aging president approaching the end of his term whose policies are mostly reactive and whose thinking is old-school compared to the dynamic leader in the Kremlin.

At the same time, polls published here recently indicate that people are moderately optimistic about the trend in Soviet-U.S. relations. Among Muscovites polled on Nov. 20 by the Soviet Center for the Study of Public Opinion, 39 percent believe that the relationship has improved, 49 percent think it is improving and 53 percent expect big results from the summit talks in Washington.

A joint U.S.-Soviet poll by the Soviet public opinion center and the Gallup Organization showed that 84 percent of Soviets -- compared to 80 percent of Americans -- believe that peaceful coexistence between the two superpowers is possible.

The poll showed, however, that only 6 percent of Soviets questioned have a positive view of the U.S. administration, while 80 percent have a positive view of the American people, according to the Soviet news agency Tass.

In a poll conducted Oct. 20 among 1,000 Muscovites by the Soviet center and Ipsos, a French polling institution, 52 percent said they thought of the United States as a declared enemy of the Soviet Union.Reagan as Figurehead

To many Soviets, Reagan, once in the foreground, has receded to almost a figurehead role, caught between what the Soviet press regularly describes as the twin guiding forces of American policy: public opinion, which favors good relations with Moscow, and the demands of the military-industrial complex, which fights them at every step of the way.

Given the dictates of Soviet foreign policy, the shift in Reagan's public image was inevitable: the Kremlin does not do business with madmen or fools. And now, with Communist Party leader Mikhail Gorbachev on his way to Washington, it is all the more imperative to have a suitable host in the White House.

In the meantime, the U.S. president, shown several times on Soviet television, is no longer an abstract imperialist but a man with a face and a voice. Many Soviets vividly recall his televised New Year's message in 1986, in particular the picture of Nancy Reagan propped on the table behind him, and remember how he stood outside without a coat on a chilly November day to greet Gorbachev in Geneva in 1985.

As for Reagan's hard-line speeches, many Soviets just write them off to pressures from the "ultrarightists" and the military-industrial complex.

"In that sense," said one worker, "Reagan is just a marionette."

Several people noted that the Iran-contra scandal and the stock market plunge have badly damaged Reagan's prestige, making him more open to Gorbachev's initiatives.

"If it were not for Gorbachev," said a 44-year-old Moscow artist who until recently was highly critical of Soviet policies, "the meeting with Reagan in Washington would not take place. He has restored a degree of trust to relations."

"I still think of Reagan as average, in terms of intellect and ability," said a 60-year-old professor, "still very anti-Soviet, but now he is willing to agree {on arms cuts} because we made it worth his while."

"Honestly speaking, I would not mind if he were to stay on for another term," said a 42-year-old office worker. "I think he and Gorbachev have managed to work something out over the last few years."

"Reagan? What do I think about Reagan?" asked one puzzled Moscow taxi driver, 32. "How would I know anything about him?" Fluctuating Perceptions

The fluctuations in popular perceptions of the Reagan administration are the result not only of changing times, but of the contradictory view of the United States as seen from the Soviet Union.

In the Soviet view, the United States is not just a country but a kaleidoscope of virtues and vices -- a bastion of imperialism with an industrious, friendly population; a land of plenty where the homeless sleep on heating grates; a democratic nation where blacks, women, peace activists and the unemployed have to struggle for their rights.

People's images of America are a jumble of the random and sparse information they receive. From the Communist Party newspaper Pravda come the cartoon figures of bloodthirsty American generals dangling politicians on a string. From videotapes, western radio, tourists and the occasional American film, comes a picture of another society where people work hard, fall in love, play loud music and shop in supermarkets.Young People's Impressions

The second set of impressions seems to have sunk in most deeply among young people. A group of 50 were recently asked their opinions of the average American. The replies, given anonymously, revealed a collage portrait that veers sharply from the gloomy, violent images on Soviet television and in the Soviet press.

"A free man" was the simplest answer, scrawled by one student on a piece of notebook paper. The others were more discursive:

"For a long time, the American people were presented to us as hungry, frozen, grate-sitting Negroes. But in point of fact, most Americans are well educated."

"The average American earns $24,000 a year, can have a car, a house or an apartment no smaller than four rooms. If things are going well for him, then he is a happy guy. If not, then he only dreams of getting rich and becomes aggressive."

"He is more responsible at work than the average Soviet, which can be explained by the fact that he is afraid of losing his job."

But he who does lose his job, noted another respondent, "drives to the unemployment office in his own car."

By overwhelming consensus, the group described the average American as businesslike and hard-working. Then the portrait begins to break up into its component parts: Americans like sports and don't smoke, have their own opinion "on all political questions," but are not much interested in "anything beyond their noses"; are patriots, maybe even a "little fanatical," "insolent" and on the whole "not friendly to leftists, in particular communists or the U.S.S.R."; are geared toward making money and tend not to be "very charitable," but are very relaxed and outgoing, fun and sociable.

What is strikingly lacking in most conversations here about America -- whether about Reagan or drive-in hamburger stands -- is any kind of context, a basic understanding of what besides money keeps America running.

People know about unemployment, but are only dimly aware of unemployment benefits, church groups or volunteer societies. They know medical care is not free, but are unaware of health insurance. The process goes in reverse: People know about what are, in Soviet terms, astronomical salaries, but have not heard that a family might have to pay $1,000 in rent a month.

The vast distance separating the two social and political systems means that references to the Bible Belt or yuppies, political action committees or superprimaries are simply incomprehensible here -- just as Central Committee plenums and May Day slogans, Komsomol meetings, Hero Mothers and vodka lines are incomprehensible in the United States.Official Caricatures

Into the void creep official caricatures and old formulas that have become threadbare from overuse, but still persist. Thus, Alexander Yakovlev, a Gorbachev ally and member of the Politburo, writes, in "On the Edge of an Abyss," about "America's tycoons," who together with the military would "bury hundreds of millions of people under the ruins of razed towns and cities with the sole aim of forcing the world to its knees."

One of Gorbachev's favorite themes about U.S.-Soviet relations is the need to break down old stereotypes, to break out of the habit of seing each other as the enemy.

And yet, by the admission of leading journalists here, this is one area where the Soviet press has yet to "reconstruct" itself. Although positive feature articles appear now and again, the main image of the West remains pretty bleak.

"The West is portrayed as a place with increasing crime rates and rising prices, drug addiction and mass unemployment. It seems they live in some kind of hell," wrote a reader in the magazine Arguments and Facts earlier this year.

Fyodor Burlatsky, a well-known commentator, wrote last May that the Soviet press let down its readers by not following important trends in the West, such as the information revolution or computer technology.

"While we were frequently patting ourselves on the back with comparisons from the postwar, prewar or even prerevolutionary periods, the whole world was rapidly developing all around us," he wrote. Yet during that time, Soviet readers' news from abroad was about unemployment and reactionary politicians, only further warping perceptions, he said in the article in Sovetskaya Kultura.

The call for "new thinking" in Soviet foreign reporting has produced few fundamental changes so far. Last month, Moskovski Komsomolets, the capital's youth newspaper, ran a review of a new book about America (the cover is a picture of the Statue of Liberty littered with dollar bills, and the book is entitled "What Do You Live on, America"), which began by stressing that the time had come to penetrate the cliches and explore America's depths.

"Democracy American-style. What is it?" the reviewer asks and answers with a passage from the book about child prostitution near New York's Times Square. "How does that kind of democracy strike you? Do you like it?" the article continues.

This determination to see the West -- in particular America -- in such black/white images has been undercut by the recent series of U.S.-Soviet television hookups that have given viewers here a glimpse of how average Americans behave and react. Judging from some of the students' responses, they do not necessarily like what they see -- "I thought the Americans were pushy" -- but at least it gives a more realistic view."Socialist Way of Life"

Stereotypes persist, nonetheless. The newspaper Moskovski Komsomolets recently reacted in horror to a brochure issued this year by a Moscow teaching institute that was offering the following poster comparing the "socialist way of life" and the "bourgeois way of life."

Under socialism appear these characteristics:

"Stability of prices, a constant growth of real income of the population; collectivism; humanism; social optimism; plan for the economy and social development; comradely interdependence; high spiritual-moral ideals; a lofty popular culture; confirmation of human values."

Under capitalism appear these:

"Rise in cost of living, prices, inflation; individualism; antihumanism, social violence against the workers; social pessimism, no faith in tomorrow; economic crises, social shocks; competition; lack of ideals, pursuit of profit; degradation of culture; neglect of the interests of the individual for the sake of money."

As Gorbachev and other Soviet spokesmen often point out, Soviet people harbor little animosity against Americans as a people, and they frequently express amazement at films such as the television series "Amerika," about a Soviet occupation of the United States, which they take as a national, rather than a political, insult.

But as some thoughtful Soviets note, the distinction made here between the American government and the American people -- confirmed in the recent polls -- is due in large measure to the continuing gap in information.

Said one Russian familiar with American politics: "It is easier to blame Reagan's link with the military-industrial complex than it is to explain the roots of the conservative religious right."