IN BERMUDA, two blacks, both regarded as black-power radicals, were convited of multiple murders. Local authorities decided that racial harmony and respect for law and order would suffer more if a stay of execution were granted. The British governor and then the British government in London accepted the decision, though Britain itself had voted to abolish the death penalty after the prerogative of mercy had been delegated to the colonial level in 1947. So the first execution in 34 years took place the other day. Riots at once exploded, causing property damage in the millions and, presumably, commensurate damage to Bermuda's tranquil image, its dearest commercial asset, and to relations between its 33,000 blacks and 22,000 whites.

It seems anomalous, a decade after the United States' own riots, to see black Bermudans expressing their community's grievances in this destructive way. Yet to the extent that white Bermudans attribute the trouble, as some still do, to a "core" of "troublesome" youths, rather than to their own obsolete social and economic practices, they invite more trouble. It was, after all, nearly 10 years ago that a commission looking into the causes of earlier racial disorders found ugly subsurface tensions fed by the fact that blacks did not occupy the position that their numbers, capacities and aspirations dictated. Too much of that indictment, it appears, is still to the point.

The British have the ultimate responsibility for Bermuda, yet since the colony is internally self-governing, they do not have the power to work for the necessary social change. This discrepancy may put steam behind Bermuda's long-mulled contemplation of independence. But whether a new political status would produce better racial policies is another question. All over the Caribbean, local politics are becoming increasingly racial. Resentment seems to be rising against the spectacle of white-run economies (and political systems) serving largely white tourists. The troubles in Bermuda - never mind that it is physically some distance from the Carribbean proper - signify tightening pressure throughout a region that too many Americans still think of, mistakenly, as one big island paradise.