ASPORADIC SERIES of armed robberies and murders, some involving tourists, has buffeted St. Croix and St. Thomas, the U.S. Virgin Islands, in recent months.

The rash of violent crimes, which began last winter in St. Croix, had earlier raised tensions on that island. But by spring most islanders had agreed that the panic among white residents on St. Croix was an unfortunate overreaction.

St. Croix hotelier and community leader Betty Sperber, who had spearheaded the campaign that brought tourism back after the industry was devastated by a backlash from the Fountation Valley golf course slayings in 1972, reported only a few hotel cancellations last winter. And those cancellations, she said, were readily filled from a waiting list.

Virgin Islands Public Safety (police) Commissioner Milton Branch has maintained that the six murders on St. Croix which shocked territory residents last January were motivated by economics not race. In a recent interview Branch reiterated his earlier statement that some of the violence has been "drug-related."

"We over-reacted," Sperber admitted.

Virgin Islands Department of Commerce figures have shown a steady decline in the number of tourists coming to the territory in recent months. From January through March air travel to the islands dropped 12.8 percent over the same period last year, and hoteliers predicted a lean 1980-81 season.

However, that trend began before the events of December and January had received national attention, and the decline is blamed instead on rising air fares and the general recession.

Then, after lull during which six FBI agents were called in by island officials to assist in the murder investigation criminals struck again -- this time on both St. Thomas and St. Croix.

On May 18, the Sheraton Hotel (now the St. Thomas Hotel) was robbed of $5,455 in travelers checks and cash by a gunman.

On May 23, a tourist from Georgia was shot and killed and one from Alabama was wounded in the hand during a robbery by two masked men outside Cathy's Fancy Beach Colony at Pelican Cove, St. Croix. A 16-year-old suspect was arrested on the scene.

That same week in various hotels on St. Thomas, two couples were robbed at gunpoint, one couple was attacked and robbed, and one woman was robbed while asleep. Three women were threatened and robbed while walking alone at night.

On May 24, Frenchman's Reef, a Holiday Inn resort on St. Thomas, was robbed by a lone gunmen of $55,000 in cash.

One June 7, four travel agents from Boston on a "familiarization tour" were robbed by two armed men at the Virgin Isle Hotel, St. Thomas.

On June 13, four tourists were robbed at gunpoint in two separate but possibly related incidents on St. Thomas streets.

Many residents believe there is a small group of hardened criminals who are responsible for much of the more violent crime committed in the islands.

The nunber of recent armed robberies on St. Thomas has convinced Sperber that the image problem has shifted to that island from St. Croix.

Word of the robbery of the travel agents "of course immediately went back to New York," said Sperber, and caused a "backlash" for the entire territory. She was not specific about how that backlash is being felt, but asserted that "anything bad on St. Croix impacts on St. Thomas, and anything bad on St. Thomas impacts on St. Croix."

Commissioner Branch downplayed the St. Thomas criminal activities. "I think that crimes against tourists are sporadic and when kids get out of school we have an increase in crime." Branch added that the police have "cleared" some cases by taking into custody a suspect they believe was involved in several of the armed robberies. He reported there were no immediate plans to ask for further FBI assistance, saying that the federal agents cannot prevent crime anymore than the police can.

Branch is quick to point out that statistics show "by and large crime in the Virgin Islands is directed against people who live here," not tourists.

In 1978 (the most recent figures offered by Branch) there were 1,443,784 visitors to the islands. Only 603 reported being the victim of any crime. And, according to Branch, 77 percent of those represent crimes against property, leaving 139 visitors who were victims of some sort of assault.

Statisically, the commissioner asserted, a statesider is safer in the Virgins than in his hometown.

In these islands the woman at the laundromat may be from Anguilla, the bankteller from St. Kitts, the carpenter from Dominica. A printer hails from Trinidad, a waiter from New York and a store clerk from Ohio. The nurse is Fillipino, the doctor from Korea. The St. Croix farmer may be of Puerto Rican descent and the St. Thomas fisherman a "frenchie" with family ties to St. Barthelemy. The roots-and-herbs peddler is a rasta man from anywhere "downisland." Almost certainly the government worker is a native St. Thomian, the taxi driver a Tortolan by birth, and the show owner a statesider or an Arab -- or, ocasionally, a native Virgin Islander.

And supporting them all is the American -- almost invariably white -- tourist, who represents the affluent life to many less-fortunate islanders.

It is almost surprising how well, for the most part, such a conglomeration of cultures mixes together in what is still a small community despite the doubling of its population in the past 15 years.