In the islands of Micronesia, young men are killing themselves at one of the highest rates in the world, researchers say, and no one knows what to do about it.

Suicides among males between the ages of 15 and 30 are so prevalent that they have become an accepted method of problem-solving in the island societies where harmony is highly prized, according to the Rev. Francis Hezel and Dr. Don Rubinstein.

''For several years suicide has been the No. 1 cause of death for youths in Truk,'' said Father Hezel, a Jesuit who has served for nearly 18 years as director of Xavier High School in the Truk Islands, where the suicide rates are highest.

Father Hezel was the first person to notice the trend, in 1977, and he wrote a magazine article on the problem. Since then, he and Dr. Rubinstein, a researcher at Honolulu's federally financed East-West Center, have collected many facts on the problem. But they do not yet have solutions, said Father Hezel, who is doing research in Honolulu as part of a year's leave of absence.