The Germans call it Schadenfreude -- a kind of secret joy over the misfortune of someone you know -- and it seems to be creeping into the attitudes of some Germans toward America these days.

To an extraordinary degree, this attitude, wherever one finds it here, is linked with the dramatic decline in the value of the dollar and in respect for U.S. economic management in the past few years. It is a phenomenon which is causing a psychological change abroad that goes far beyond the treatment of U.S. financial woes as purely an economic problem.

The effect of this decline here ranges from the detection of a new touch of occasional German arrogance to the gradually changing face of the American establishment in Germany as more U.S. businessmen go home and more Europeans replace them in managing U.S.-owned subsidiaries.

The combined, long-term impact is hard to judge. But interviews with mamy Americans who have lived or worked in West Germany for much of the postwar era suggest that it is likely to be important.

"The big change is the dollar," says Robert Lochner, head of the U.S. Chamber of Commerce in West Berlin, "and the psychological effects are very much underestimated. Jokes about the dollar are always good for laughs at Rotary Club luncheons these days," gatherings that in West German cities are now attended by far more German than American businessmen.

"It's not a hostile laughter but rather a little bit condescending. It's a smug reaction, a combination of sympathy mixed with glee, particularly among some of the old ones who remember having to work their way up again after the war and now look at us not as big brothers but as weak cousins. It's balanced, of course, by their continued military dependency on us," Lochner says, "but I think it definitely has made inroads on German fellings of depending on us."

In Duesseldorf, an American banker sees it slightly differently. "The Germans are aware of how good they are doing, so, by default, they have reason to be proud. It's sort of a self-confirmation in commercial circles that what they are doing is right.

"It is more among the man in the street," he adds, "that you really find the Schadenfreude , a real lack of honest compassion toward the U.S., even of the kind that Americans once felt for a devastated German enemy."

Mixed into this, the banker says, is another element that cannot be left out in trying to assess where America really stands in Germany today.

"Regardless of the economic aspect, American influence on the German mentality has diminished because there is no figure in the U.S. anymore who Germans really look to. President Carter is viewed here as weak, even compared to Johnson or Nixon, and as not able to keep pace in terms of political leadership with Chancellor Helmut Schmidt," so this feeds both the new German self-assertiveness and the diminution of U.S. influence. "Somewhat Irrelevant"

IN BONN, an experienced American diplomat says the United States "has become somewhat irrelevant here but in an ambivalent way. We are just as relevant as ever in the security sense," a reference to the continued presence here of the 200,000-man U.S. Seventh Army, "but for 25 years we were also preeminent here in an economic sense. Vietnam, Watergate and the economic weakening of the U.S. changed that and have produced today's ambivalence.

"The European monetary system" -- the just-formed, eight-nation currency group fathered mostly by Schmidt -- "is the symbol of that. It reflects the perception that American economic leadership and the American currency, the symbol of national prestige, are both lacking," the diplomat said.

"It also doesn't help to have an American ambassador running around Germany exuding so much optimism that the American economic problem is all under control now," says a U.S. business executive in West Berlin. "You can't sell that to educated Germans anymore."

Diplomatically, things are changing, too. A leading figure within Germany's Free Democratic Party, part of the ruling coalition here, remarked privately that at a recent breakfast gathering of top party strategists, the discussion strayed onto a surprising point: Many party figures said they and their colleagues around Germany seemed to have much less contact with American officials in Germany these days.

The problem, the party figure said, was compounded by less expertise on German affairs within the Carter administration in Washington than in previous administrations, a widespread complaint throughout German diplomatic circles. The Cultural Impact

I SIDE FROM the U.S. Army, the other visible reminder of the enormous American involvement in West Germany for the past 34 years was, and still is, American business and culture.

American music, dance, jeans, movies, television series and many other things continue to flood the West German scene. A walk through any major German city will be punctuated by constant reminders of American products and entertainment, a trend which, if anything, has been accelerated in the past few years by the injection of U.S. fast food chains and ice cream parlors.

"What is happening," says a Frankfurt banker, "is that Germans are becoming even more aware of American products and less aware of American leadership."

Big American firms like IBM, Xerox, Texas Instruments, Ford, 3M, Opel division of General Motors, the big banks and others are doing very well. But Goodrich, Firestone, U.S. Steel, ITT, Gulf, Occidental Petroleum, National Biscuit, Singer, NCR, Beckman Instruments, Amphenol and several other firms all have either shut plants down, are expected to, or have otherwise withdrawn from some part of the German market recently, U.S. businessmen report.

In May, Chase Manhattan Bank, though successful in commercial dealings, shut down 29 small branches of new family bank concept that lost $25 million here. Americans Leaving

MOST IMPORTANT perhaps, over the long haul, is that Americans are going home.

Four years ago, says Paul Baudler, head of the American Chamber of Commerce in Frankfurt, there were more than 500 top-level U.S. executives in Germany running U.S.-owned firms or subsidiaries. Today, he estimates, there are only about 200 key executives left.

Some of this decline is natural. In the 1960s, American dollars and investments swamped Europe, touching off European fears of total American domination -- something that never really happened. With the wave came U.S. executives to make the big investment decisions and start up the European subsidiaries. Now, the investment tide is reversed. Germans are buying chunks of America. The plants here are functioning smoothly. Germany is too expensive for much new U.S. investment and so some of the executives are being withdrawn.

But a major factor in this withdrawal also is the roughly 30 percent drop in value of the dollar in comparison to the German mark in the past two years. This has made it very expensive for U.S. firms to keep U.S. executives in Germany.

The big firms say that wherever an American is needed, they will always pay the price to have one.But in fact vast numbers of executives -- especially at middle levels -- are being replaced by European managers who don't need to have cost-of-living allowances, school tuitions and foreign taxes paid for by the home office.

One result is that huge U.S. firms operating in Germany today -- Dow, DuPont, Ford Exxon, Mobil and many others -- now have either no Americans on their top executive boards in Germany or perhaps just one at the top, industry sources say.

Another result, say many businessmen here, is that replacing so many Americans with Germans or other Europeans will eventually further erode American influence in the world and lose the continuity for American business. Americanized Leaders

BALANCING some of the subtle strains in German-American experiences these days is an equally hard to define link that is generally viewed as positive. That is the thousands of West Germans now assuming leadership roles in industry, politics, education and the military who in one way or another have been directly exposed to American society through some part of their education, work or travel.

For example, some 8,000 Germans since 1953 have studied in the United States under the Fulbright exchange program alone. Some 2,500 German air force officers went through flight school in Texas. Several members of the German federal parliament and ministers in state government are American-educated.

Two potential future candidates for chancellor from the opposition Christian Democratic Party -- State Finance Minister Walther Leisler Kiep and parliamentarian Kurt Biedenkopf -- "are so Americanized it's striking," says American author George Bailey.

Yet, as Ullrich Littman, director of the German Fulbright Commission, points out, there could also be a break in this so-called Americanization process with the German generation of the Vietnam-Watergate era, when reservations about U.S. values were widespread.

Bailey, a long-time resident and specialist on Germany, believes the U.S.-German relationship "is more natural now. My feeling is that Germany is still an occupied country, as of course it is in the East, too. But the West Germans can act more unilaterally now. There is a pretty good partnership with the U.S. The relationship has always had its ups and downs. But they are used to us now and the deeper the relationship is, the less it strikes you superficially. We are their salvation and they know that. There is no prospect for a real change." CAPTION: Illustration, "Fresh, spirited American troops, flushed with victory, are bringing in thousands of hungry, ragged, battle-weary prisoners..." (News item); Copyright (c) 1945, Bill Mauldin; Picture, The dollar has dropped 30 percent in the past two years.