About $350 billion in U.S. currency is thought to be floating around foreign countries, more than the amount circulating within the United States. And the amount is rapidly growing.

First Union Corp. sees gold in those numbers and in March plunged into the business of trading international banknotes. It sells dollar bills to foreign banks and brokerages and resells the foreign banknotes it acquires to financial institutions in the United States and elsewhere.

Profits are made from the difference between what First Union pays for the bills and what it charges, plus an array of fees, such as for transporting the notes.

Obviously, the Charlotte, N.C.-based bank is optimistic about the business, but more entrenched competitors say they fail to understand why First Union would enter a business with very low profit margins.

First Union's optimism stems from its belief that demand for currency- both dollars and foreign banknotes-will surge in coming months and years.

This year, for example, the bank expects people around the world to withdraw cash from banks to protect themselves from disasters that could arise as a result of year-2000 problems.

Another, longer-term reason for First Union's rosy view of the bank-note business includes the increasing use of U.S. banknotes within foreign countries. Argentina, for example, is considering giving up its peso and using U.S. dollars as its currency. Several Caribbean countries - including Cuba-use the dollar as their own currency.

The dollar's popularity stems from the political and economic stability of the United States, assuring people around the world that the dollar will keep its worth, says Jeffrey B. Pruiksma, staff director at the Federal Reserve Bank of New York. For that reason, the dollar is universally accepted, more so than any other currency.

When a country's political and economic systems become shaky, many of its residents seek safety in the dollar. Russians, whose country is mired in political and economic turmoil, are believed by experts to be among the largest holders of U.S. $100 bills. This global trend is not expected to abate.

First Union also says more people are traveling internationally and that the number of "unbanked" consumers around the world is growing. These people need cash, and the dollar is more likely to keep its value than most other currencies.

The banking company also forecasts a bonanza in the bank-note business in 2002, when 11 nations of the European Union withdraw their old currencies and replace them with the euro. Much business already is denominated in euros, but no euro banknotes have yet been printed.

No one knows precisely how many dollars are outside the United States, but the Fed's Mr. Pruiksma estimates that about 60% of all U.S. banknotes are abroad. Any way it is counted, that is a lot of dough.

The amount of U.S. dollar banknotes in circulation climbed to $525 billion at yearend 1998, from $122 billion in 1980. Including major European currencies, such as the German mark and the French franc, some $1 trillion worth of banknotes are circulating, says George M. Doolittle, senior vice president and managing director in charge of First Union's bank-note program.

"People talk about the cashless society but there's more cash out there than ever," Mr. Doolittle says.

First Union's decision to enter the bank-note business is designed to leverage the global correspondent banking network it inherited when it acquired Philadelphia-based CoresStates Financial Corp. last year. CoreStates had correspondent relations with about 5,000 banks around the world.

Shipping and processing banknotes is much like the check-processing and documentary collections First Union already handles, Mr. Doolittle said.

"We already have the infrastructure, the customers and distribution in place," he said. "So for us, the additional investments are not significant."

Profitability in the low-margin business depends on volume, he said, and he expects the bank's correspondent network to create high volume.

"This is an economy-of-scale business," Mr. Doolittle said. "The more you ship, the more you lower your costs.

First Union has hired a small team of bank-note dealers in Bahrein and staff from GWK Bank NV, an Amsterdam-based unit of Fortis, the Belgian- Dutch financial conglomerate.

Some analysts are skeptical.

"This fills out the menu of services they offer, but whether or not it succeeds depends on the kind of effort they will put into it," says Katrina Blecher, a banking analyst with Brown Brothers Harriman in New York. "Until that becomes clear, we won't know whether it was an intelligent decision or not."

Thomas Weiner, managing director at Republic New York, said he is perplexed about why First Union would want to enter the field.

Republic, he said, charges only $5,000 to ship $10 million in banknotes from one vault to another halfway around the world. And big customers get a discount on that.

"There is going to be a shakeout in this business," Mr. Weiner predicted.

First Union may also be underestimating the costs involved. Though it does have a network of correspondent banks, it still needs to invest millions in warehousing, labor-including foreign exchange traders-security, transportation, and insurance.

Getting the logistics right, he added, is extremely tricky. And even if the actual volume of notes in circulation is growing, any new entrant is going to have to grab most of its business away from other, better established banks.

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