In the turmoil that gripped this country in the fall of 1956, when a popular uprising was crushed by Soviet tanks, a 20-year-old economics student named Bela Bakonyi was among the 160,000 Hungarians who fled across the borders to the West.

Today, Bakonyi, an American citizen, is back in his native Hungary and taking part in what may be the start of a much more peaceful, yet also revoluntionary development here -- the increasing status of Budapest as an international financial and trading hub between the West and Eastern Europe.

Bakonyi, who says he is "not a political person," just opened the first branch office for an American bank in Hungary and become the first permanent resident U.S. businessman in this communist capital.

The bank is a branch of the National City Bank of Minneapolis, and its establishment here is viewed by Hungarian and U.S. officials as a progressive move aimed at furthering East-West trade and cashing in on it.

Trade with the six nations of the Warsaw Pact outside of the Soviet Union -- Bulgaria, Czechoslovakia, East Germany, Hungary, Poland and Romania -- amounts to only about 1 percent of U.S. foreign trade and 6 percent of the East's trade with the West. It is, nevertheless, a booming and expanding market about which many American firms know very little.

Between 1970 and 1978, according to official U.S. statistics, American trade with the East has increased six-fold and is now running at more than $2.5 billion a year. About two-thirds of this is in agricultural commodities and the rest manufactured goods, often of high technology.

Hungarian Foreign Ministry officials view the bank branch here as "important and significant because it means there is real interest now in some parts of the U.S. business community.

"Both governments did their best to improve the climate in terms of human contacts," and the fact that the United States granted Hungary most-favored-nation tariff status improved the trading climate, "so now it is up to business," one official said.

The fact that a medium-sized American bank is the first to open here is also "maybe better and more natural" than one of the giants because it matches the scale of Hungarian enterprises, he added.

Of all the countires of the East, Hungary has the currency that is probably closest to someday becoming convertible to Western money. Budapest also has a collection of some of the world's more respected bankers within the Hungarian National Bank, especially its deputy chairman, Janos Fekete.

On Friday, Fekete and his colleagues presided over the signing of another agreement, the first of its kind in East Europe.

The agreement creates a new institution called the Central European Bank, Ltd a joint company owned by individual banks in Italy, West Germany, Austria, France, two in Japan, and the Hungarian National Bank. The combined assets of the participating banks, sources here point out, is about double those of the Bank of America.

The new setup is unique in several respects. Its establishment here signals a move away from traditional European trading centers such as Frankfurt. It also is another sign that Hungary is reaching out to join the world economy and of Budapest's growing status in financial circles.

While the National Bank of Hungary holds a 34 percent interest in the joint company, it does not hold a controlling interest, something that is also unique for a communist country. Each of the other shareholding banks has 11 percent, so that there is in effect no government control at all. "It is something like an offshore bank," one banker here says.

Like the American bank, the idea is to facilitate international trade, only the geographic charter is broader, taking in many other areas of the world.

There are two other American banks in Eastern Europe. New York's Manufacturers Hanover Trust has a branch in Bucharest, Romania, and a Chicago bank has an office in Warsaw, Poland, only without, it is said, a resident American manager. There are many U.S. bank branches in West Germany whose representatives travel in the East, but live in the West.

Nevertheless, the area still is largely virgin territory, says Bakonyi, who notes that "you can't really do the market research on Hungary from the U.S." In other words, it is hard enough to do business in the East taking even west European businessman many years to develop contacts and deals, without actually living there.

U.S. trade largely follows U.S. politics, with countries such as Poland and Romania, which have generally good relations with the U.S. getting by far most of the trade. East Germany, Czechoslovakia and Bulgaria are more distant politically and commercially.

Hungarian-U.S. relations are good, yet trade is small, about $167 million last year. Hungarian officials here say $600 to $700 million annually "should be more normal."

Hungary's problem, however, is similar to the rest of the East; communist bloc countries have serious deficits in their trade with the West and trouble selling their products in the West in order to gain hard currency to pay for their imports.

But the Hungarians are in the process of a new economic reform program which, in the short term, is apt to be painful for its citizens and probably reduce the standard of living here. Nevertheless, over the longer term most economic specialists believe it will strengthen the country's economy and productivity.

Hungary already has more Western elements in its economic policy than the rest of the Warsaw Pact and the new plan will increase that tendency.

The first step was a sharp rise in consumer prices in July, which has produced some grumbling but no unrest. The idea is to bring local prices more into line with world prices.

On top of this is an effort to make the country more productive both by actually laying off people in industries that are vastly overstaffed and even shutting down inefficient firms. This is unheard of in the East, where full employment is an integral part of official propaganda. The Hungarians, however, say they still will not really have unemployment since labor in this country of almost 11 million people is scarce. The problem is that many operations have far too many people while others are short. Thus, an attempt will be made to shift the labor force rather than start writing welfare checks. w

Finally, the idea of piecework is being introduced here, something that could shakeup a work force that is not used to be being paid on the basis of how much they turn out.

The most efficient plant in the country, sources here say, is the factory turning out American-licensed blue jeans under a piecework formula.