The latest wave of Cuban refugees directs attention to a major new development in American life. That is the transformation of southern Florida, largely because of the Cuban-American community here, into a significant international center, a crossroads for the Caribbean.

Fidel Castro set the present flow of refugees in motion apparently in order to unload at least some of the Cubans dissatisfied by recent economic difficulties. The initial American response, framed by the national security community in Washington, was to try to stem the tide by applying to the letter tough immigration laws.

In line with that approach, the captains of the first ships bringing over Cuban refugees were subjected to heavy penalties. But then the local Cuban community entered the picture.

Scores of Cuban-Americans set out in small boats to bring relatives and friends to this country. Their spontaneous action was then coordinated under the direction of a local Dade County official, Sergio Pereira. Over $2 million in food and clothing was raised for the newcomers. Elaborate health and legal services were made available. Hundreds of volunteers were mobilized to help them through the bureaucratic maze of immigration. "I don't know any other community in the country," a White House official now working here said, "that has the resources, the motivation and the organization to do what the Cuban-Americans did."

Gov. Bob Graham backed up the local effort with state services. No doubt his action was heavily motivated by humanitarian considerations. But there was also a sense, widespread in the business community here, of what the Cubans contributed to southern Florida. In a telephone interview the governor said:

"I was born in Miami in 1936, and I grew up in Miami, and I remember that the city slogan was 'Gateway to South America.' In fact we were the gateway for south Georgia. But the advent of the Cuban refugees in 1960 made the slogan a reality. Now Miami is an international financial center. About a hundred corporations have their Latin American headquarters in Coral Gables. Miami has ceased to be a southern city. It is a cosmopolitan capital."

President Carter had to follow the local lead. Not only because Graham is a vital supporter in a state that could vote for Ronald Reagan in the fall. In addition, the action of the Cuban-American community made any other policy impossible. "We cannot exactly have the Coast Guard sinking mom-and-pop boats," one federal official here put it.

So Washington switched signals. The refugee problem was moved away from the national security community and given over to the domestic policy side of the White House. Florida was declared a disaster area. Tom Casey of the Federal Emergency Management Agency was sent here to coordinate the multitude of interested federal agencies -- Immigration, Social Security, FBI, CIA, Coast Guard, State Department and others -- in a drive to expedite the processing of the refugees.

The operation is still far from perfect. While rapid in some places, the flow is agonizingly slow in others. Some criminal elements slip by the screening process, and probably some espionage agents. Federal officials, and some local members of the Cuban community, are worried that the new batch of refugees may lack the skills and drive that did so much to establish the batch of 1960. There is no telling how many Cubans Castro will drive out, and a diplomatic effort is under way to share the burden with other countries.

Some countries of the white Anglo community here resent the treatment accorded the refugees. One local talk show has revived the old epithet "spic," and aired the view the Cubans ought to "go to Alaska." A low-level federal official complained to me about the "unwillingness of Cubans to learn English -- as if it wasn't good enough for them." A National Guard officer told me: "This is going to hurt Carter politically."

Black leaders have contrasted bitterly the receptive attitude shown toward the Cubans with the onerous conditions imposed on illegal immigrants from Haiti. T. Willard Fair of the Urban League acknowledged to me that Cuban enterprise had been good for black employment, and that most members of the black community didn't care all that much about the Haitians. But he observed that the U.S. government had shown "flexibility and ingenuity in dealing with the Cubans," while being "unsympathetic to the Haitians."

But all this only underlines the emergence of Miami as an international center. Southern Florida has become a focal point for the whole Caribbean. The influx of people -- from other islands and some mainland countries, as well as Cuba and Haiti -- is bound to swell.

The critical question is whether the region can organize its social relations in ways that make the crossroads something of a melting pot.