For nearly a week, rumors have spread along the quiet streets of this tiny British dependency -- talk of retribution, of hostages, of toppling governments and of British warships rushing to the scene.

Christopher Turner, the British governor, has tried to calm the islanders and has urged them not to "take to the streets."

This island -- the government seat for the Turks and Caicos Islands -- has been in turmoil since last Tuesday, when Turner announced that three of its top elected officials had been arrested in Miami by U.S. drug agents in connection with a massive cocaine- and marijuana-smuggling scheme.

For the next day, islanders watching the local television channel saw the officials led away in handcuffs. All three are still in prison in Miami in lieu of bail set between $1 million and $2 million.

The three are Chief Minister Norman Saunders; Stafford Missick, the minister of commerce and development, and Aulden (Smokey) Smith, the deputy public works minister and parliamentary secretary.

The officials are expected to be charged with racketeering and conspiracy to import cocaine -- charges that carry a maximum penalty of 30 years in prison. The men allegedly agreed to provide protection for drug traffickers using the islands as a refueling and transshipment stop.

In the past there has been little tension between the predominantly black islanders and white British government officials. But the arrest of Saunders, Missick and Smith, who are black, may have changed that.

Turner lives at Waterloo, the official government house at the southern end of this seven-mile-long island.

His official car is a black Lon- don taxi painted with the royal Turks coat of arms.

Asked about rumors of approaching British warships, Turner declined to comment.

Angus Mackay, sent here by the British government last week to assist Turner during the crisis, said, "In British dependencies, there are always contingency plans available in the event they should become necessary to prevent a disturbance or disorder . . . . The British government never goes into detail on these plans."

Turner announced at the time of the arrests that the British government and the Royal Turks and Caicos Police force, which reports to him, had cooperated in the investigation by the U.S. Drug Enforcement Administration. In fact, Great Britain contributed $750,000 toward the two-year DEA investigation here.

The British involvement has caused hard feelings here.

Nathaniel (Bops) Francis, Saunders' deputy, went on national radio Saturday and asked islanders not to resort to violence, but he also asked them to contribute toward a bail and defense fund for the jailed officials.

Robert Hall, minister of health, education and welfare, was not so restrained. He referred to the "gathering vultures" and criticized the British role in the investigation.

In the past several days, word has spread that island activists may be considering taking a hostage, possibly the governor or an official of one of the British banks here, to exchange for Saunders.

Several nights ago, in a local bar, two U.S. reporters were accused of being DEA agents and searched for weapons or hidden microphones.

These islands -- dotted with small, whitewashed houses with corrugated metal roofs, surrounded by bougainvillea, hibiscus, sandy beaches and clear turquoise water -- are no stranger to chicanery and intrigue.

Discovered in 1512 by Ponce de Leon, they served for many years as a hideout for pirates.

As recently as 1982, Miami gas station owner Bernard Sansaricq used the islands as a staging area for an ill-fated invasion of Haiti, about 100 miles away.

The Turks and Caicos Islands do not appear to be a likely site for a revolution.

The dependency is made up of 42 islands, only eight inhabited, covering about 192 square miles. The population of about 7,500 includes native islanders, known as "the belongers," and several hundred British, American and Canadian transplants, known as "the expats."

Located southeast of the Bahamas and north of Haiti and the Dominican Republic, the islands have no industry. The salt mining that once supported them collapsed in the mid-1960s. There is some fishing for lobster and conch, and many islanders work for the British or local governments. The Turks and Caicos have shown no signs of seeking independence from Great Britain, which provides financial assistance.

Islanders acknowledge that their islands have been used for years as a transshipment point and refueling stop for drug-laden planes traveling from Colombia to Florida. That traffic has picked up in recent years for several reasons.

The United States abandoned Air Force and Navy bases at each end of the island several years ago, taking away a major source of funds and creating a need for new revenue.

In addition, the island has become a haven for companies seeking to avoid taxes. There are no corporate, personal property, personal income or real estate taxes in the Turks and Caicos, or any requirement to disclose income or property ownership. As a result, about 5,000 companies have set up headquarters here -- at least on paper.

The tax laws make the islands an ideal place for laundering drug money and other illegal profits.

Eight runways and landing strips are scattered among the islands, including three international airports capable of handling a Boeing 727.

Many islanders apparently have seen little harm in earning money by helping drug smugglers.

Lewis Astwood, a political opponent of Saunders and a fellow member of the Turks and Caicos Legislative Council, said cocaine use among the islanders is relatively new and that most do not realize how valuable the drug is when it reaches the United States or how dangerous the traffickers can be.

One local government employe, who asked not to be identified, said the islanders generally obtain cocaine for their own use by raiding trafficking planes that lie over at the airport. He said they then run off with cocaine and share it with friends.

About two years ago, he said, five angry drug traffickers armed with machine guns showed up at the South Caicos International Airport looking for the missing cocaine. They shot up the airport but never found the drugs.

It was at that airport that Saunders allegedly planned to provide a haven for traffickers en route from Colombia to Florida.

Saunders owns the airport's fuel concession and the building housing the control tower and switches for the runway lights.

According to a DEA affidavit filed in U.S. District Court in Miami, Saunders, Missick and Smith told agents they would provide protection for the smugglers to move as many as 800 kilos of cocaine a week though the Turks and Caicos Islands.

It was agreed, according to tapes and videotapes of meetings between the three men and DEA informers and undercover agents, that the cocaine supplier would be paid $375,000 per trip and the three Turks and Caicos officials would split $250,000 per trip.

According to the affidavit, Saunders and Missick also offered to assist by "laundering millions of dollars through friendly banks located at Grand Turk Island."

Jack L. Lloyd, No. 2 official at the Miami DEA office, said the three are not eligible for diplomatic immunity because they were not conducting official business in the United States.

DEA agents involved in the investigation say that on such small islands it is likely that virtually everyone knew about the trafficking.

"Everyone is related," said Bob Joura, one of the DEA undercover agents who posed as a drug dealer in the Turks and Caicos. "South Caicos is a very small island."

He said that drug flights occurred at night, when the airport is officially closed, and that a car would be driven up and down the runway to chase off wild donkeys.

There was no interference from local customs officials. "We made a stop in one of the islands to refuel," Joura said. "A customs officer came up and asked if we were here for a vacation or to invest. My pilot told the officer that he was a drug smuggler. The customs official put his arm around him and said, 'Come with me.' "

Despite charges by some of Saunders' supporters that he was framed by the DEA, the governor has asked for his resignation and is sending Saunders' deputy to Miami on Tuesday to confer with him.

Saunders' Progressive National Party has an 8-to-3 majority over the Peoples Movement Party in the legislative council. But with three members in jail, that majority has been reduced to 5 to 3.

Astwood said his party will push for new elections as soon as possible. "If this government remains, there isn't anything good that could happen to this country," he said.