Millions of dollars change hands each day in this slow-paced speck of a country, whose 450 banks have turned it into the fastest-growing tax haven in the Caribbean.

There are 18,000 foreign corporations registered here, more than one for every resident of the Cayman Islands. Many are lured not by the warm sun and quiet beaches, but by the tax-free environment and business secrecy laws that make it easy for wealthy Americans to avoid income taxes.

The kind of companies Americans invest in is illustrated by the directory of a modest two-story building here. There are 201 corporate names in all -- from Ascot Trading Co. to Zeus Ltd. -- but they have no offices inside. Most of the building belongs to the Bank of America.

Such companies provide a financial lifeline for this British colony 460 miles southwest of Miami, which lives off tourism and tax avoidance. Its only other industry plummeted after the United States banned turtle imports in 1978, yet it has more banks per capita than anywhere in the world.

"Cayman has become the Switzerland of the Caribbean," said Orren Merren, a Cayman attorney who has represented the islands in Washington. "It's a British colony without a lot of social tension, it's a good location and the banks themselves may get some tax benefits."

Cayman officials dislike their reputation as a money-laundering center for drug dealers and agreed to cooperate with U.S. narcotics investigations last year. However, anyone caught disclosing financial transactions here without official sanction faces a two-year prison term.

Merren noted that tax evasion is not a crime here and that "one country is not obligated to help another country supervise the collection of its revenues. The fact that people are evading taxes . . . that's between them and their government, or them and their conscience."

A British Embassy spokesman said that Britain is concerned about abuses of Cayman banks and has been discussing the problem with Cayman and U.S. officials.

U.S. authorities say the flow of illicit cash here -- up to $10 billion a year, by some estimates -- would not be possible without the cooperation of major banks. Most of the Canadian, British and Swiss banks in Grand Cayman will accept large deposits from Americans with few questions asked.

At the Bank of America's subsidiary here, an officer told a visiting American that he could not open an account for less than $250,000. "If it's $50,000 or $100,000, we figure people are just bringing the money here and trying to evade taxes," she explained. But she added, "If you go through a lawyer and form a Cayman corporation, then it's all right."

That can be done in a day at the Registrar of Corporations, where the walls are adorned with 20 pages listing newly formed companies, including such ventures as Garmi, Garmo and Garmu. All you need, Carol Walker explains from behind the counter, is a list of shareholders and a registered office here. But that can be nothing more than a post office box and a local lawyer to answer your mail.

"I could have this space and cover a thousand companies," Walker said.

Some American tourists are intrigued by local magazine ads touting "All You Need to Know About Tax Havens." They come to the videotaped seminars held three times a day at the Holiday Inn for a tax-deductible fee of $25.

Although the film was produced by the United States Tax Planning Service (USTPS), which is under investigation by the Internal Revenue Service, it is still a popular draw.

The curtains are drawn in a small room, and USTPS founder James G. Bryan appears on the television screen. "Welcome to the fourth largest financial center in the world," he says. " . . . I'm Jim Bryan, and I'm the author of the U.S. Tax Planning Concept."

Music rises and an eagle's-head logo flashes on the screen as a narrator intones: "The U.S. Tax Planning Concept -- dedicated to the preservation of wealth and private property."

"The U.S. was born because of a tax rebellion," says Bryan, an avuncular, white-haired man whose current whereabouts are unknown. "When the government gets aggressive and oppressive with their taxes as they are doing today, many people look for a refuge."

When Germans put their money in Swiss banks in the 1930s, he says, "The Gestapo put on a great move to try to crack the bank secrecy laws in Switzerland. Today, there are new forms of Gestapo, and those new forms of Gestapo in most countries are called tax collectors."

Bryan describes how someone earning $200,000 could cut his $68,500 tax bill to zero by setting up an offshore corporation and investing in such things as diet plans and oil wells. He draws boxes and arrows to show how a taxpayer can put his money in a Cayman company, under foreign directors and trustees, and still direct its flow.

After the showing, viewers are offered a free consultation at International Services Group Ltd., which operates out of the same office once used by USTPS. The company, which puts out a booklet called "Tax Haven Journal," also has the same phone number, post office box and eagle's-head logo as USTPS.

Lynford R. Evans, director of International Services Group, said his new company, unlike USTPS, does little tax work. He said he uses the seminars to attract potential clients.

Evans, a thin, bearded man who laughs easily, said he was still using the Bryan videotape because he couldn't afford a new one. "The only thing we have that's making any money is the Holiday Inn seminar, so why chuck it?" he said.

Evans said the IRS has singled out his former company for practices that are common in his native country.

"That's how the Cayman Islands survives," he said. "We're a tax haven . . . . Do you want to do business with someone down here, or do you want to give 50 percent of your income to the IRS?"