The bombs had been going off for months. A mysterious organization known as the GLA -- Armed Liberation Group of Guadeloupe -- was claiming responsibility for a steady string of kidnap attempts and dynamite blasts in the name of independence for this tropical Caribbean department, or province, of France.

The airport was bombed, the government radio station was blasted, explosive charges were found beneath the car of an Air France executive. In all there were as many as 17 incidents. Miraculously, only one person was killed.

Anywhere else such activities might have provoked grave international concern, especially with growing worries about Cuban-inspired terrorism in the Caribbean. But Guadeloupe and its sister island of Martinique have established such a reputation for stability and alluence in this generally unstable and impoverished region that the outside world seemed hardly to notice.

The members of the liberation group appeared to be rebels without plausibility. Yet there are serious problems here and the group may represent a more serious threat than either the French or the Americans interested in the area have admitted.

On Jan. 4 the fashion house of Chanel was blown up in Paris and the group took credit for carrying the fight to the mainland. Days before, the group had issued a communique warning "the French" on Guadeloupe to get out by Dec. 31, 1980.

"The French who stay," said the communique, "will take the responsibility for what will happen, the 1981 will be a bloodier year than Guadeloupe has ever seen."

On Martinique, which has its own GLA, the Palace of Justice was burned and a similar ultimatum was issued. Virtually no one has left, however. Tourism in the islands' resort hotels remains good. The people of Guadeloupe and Martinique continue to react to the liberation groups with a mixture of disbelief and a strong tendency to dismiss the whole affair as somehow unreal and unimportant.

Yet alienation is real on these islands, and it is much the same kind of political, economic and cultural alienation that has fostered violent discontent elsewhere in the Caribbean Basin. There is potential for serious, even violent, strain in the fabric of what one resident called this "mosaic" society of blacks, East Indians, native-born and European whites.

Although few people believe the Armed Liberation Group has more than a handful of members, it has worked hard to exploit the islands' tensions and paradoxes and it, or a group like it, could yet succeed if provoking major confrontations.

Some residents fear, moreover, that the conflicts could spill over onto the French mainland, where a newly resurgent racism has already created troublesome problems.

Some Guadeloupeans say they think the GLA is finished. The group stole a large quantity of dynamite from a construction site last spring and now perhaps it has run out. Meanwhile, the military police have been reinforced, checkpoints have been set up on rural roads and antiterrorist specialists have been brought in from Paris. The French government, belatedly, is talking about serious recognition of the islands' cultural differences.

The official line and attitude toward the islands remain strong, however. Guadeloupe and Martinique (as well as French Guiana on the South American mainland) are not just French, they are a part of France. Since they became overseas departments in 1946, their residents have had all the political rights and privileges of their compatriots in the Metropole, as continental France is called.

Such status has brought unprecedented prosperity. Citroens, Mercedes-Benzes and Peugeots jam the streets of Pointe-a-Pitre and Parisian clothes fill the windows of its shops.

Race is not supposed to be a factor. A black "creole" has the same rights and opportunities as a native-born white beke (pronounced bay-kay) or a mainland-born metropolitain.

Differences do exist, however, along with tensions.

"The colonialist system is what has shaped this island," said one successful creole business executive here. "But the French are different from other colonialists. They want to be loved for their own sake. The French are trying to erase the differences by making you like themselves.

"But if you are trying to raise somebody up to your own level without recognizing his identity," the executive continued, "one day he is going to say 'Hey, but I'm not you. I'm myself.' And I believe that is what is happening. Having this psychological attitude plus the volcanic state of the economy, you have the fuse and the bomb."

It is obvious that for all the paper guarantees and all the centuries of ties to France that effectively isolated them from the now-independent, English-speaking islands that surround them, the French Antilles are not exactly France.

The shantytowns that wind through the outskirts of Pointe-a-Pitre are not France. Neither the descendants of black slaves nor the white scions of the slaveowners feel altogether French.

There is a common joke that when someone goes from Guadeloupe or Martinique to France he is Antillais. When he goes to New York he is French.

The societies of Guadeloupe and Martinique have proved in the past to be as unexpectedly explosive as the Soufriere and Pelee volcanoes that dominate their idyllic landscapes.

In 1967 racist remarks by an employer during a labor dispute triggered riots in Pointe-a-Pitre that left scores of people injured and dead.

Since then, several independence movements have sprung up as legal parties, although their following is mainly among the islands' intellectuals.

These independentistes find themselves caught facing the economic reality that confronts virtually all the microstates of the region.

The economies of Guadeloupe and Martinique, as they have evolved, are totally dependent on France.

The minimum wage is the same as in continental France, which makes it much higher than anywhere else in the Caribbean, but completely out of phase with the islands' productive capacity. Sugar, the principal crop, sells even at today's high prices for less than it costs to produce here.

Meanwhile, Guadeloupe is importing six times more than it exports, according to customs figures, and Martinique is in a similar position. The several independence parties recognize this problem but are unsure what could or should be done about it.

"They want to govern the island but with the money of France," said Michel Reinette, a Guadeloupean journalist.

That money is substantial. French subsidies to Guadeloupe in 1979 reportedly amounted to nearly $37 million. Almost $32 million went to Martinique.

Yet there is more than 25 percent unemployment and for many young people the only visible future is in France. By some estimates there are as many as 600,000 Antillians competing for jobs there, while only about 800,000 live on the two islands.

"There is a big risk," said one concerned young activist on Guadeloupe, "that if there are more bombs, if the GLA kill someone else, the people in France will say the Antillais have to go back."

Right-wing reaction is already surfacing on the islands. A group called the Civic Action Service, first formed in the 1950s by conservatives sympathetic to the French Algerian colonists, has re-emerged and with it a semisecret organization called the Guadeloupean Armed Defense Group, vowing to "protect French women and children from blind terrorism."

"Almost everyone here is armed," said an older beke, "and if anyone comes, we shoot. I have a .357 Magnum by my bed."

Such an environment would seem to be a perfect target for subversion. But the level of Cuban involvement is considered very low.

Fidel Castro's revolution has its sympathizers. The Jose Marti cultural center in Pointe-a-Pitre is full of pro-Cuban literature. Its director is Michel Bangoud, the communist brother of the city's communist mayor. The party is 30 years old here, legal and successful in local elections.

"We take our example from Cuba, which has proved it is possible for a small people to make a place in the world," Bangoud said.

Nevertheless, U.S. diplomats in the area who are concerned about such things said they believe that the revolutionary impulse that exists here like everything else has a Gallic flavor. They note the high number of terrorist incidents in France, inflicted by dozens of different groups.

"Where the radical influence comes from," said one diplomat, "is not rom Cuba, but from Paris."