THREE HUNTERS <i> by William Harrison (Random House: $16.95; 250 pp.) </i>

The African landscape, and Kenya’s in particular, seems to inspire rare passion in people who have lived there. In his third novel set in Africa, William Harrison tells a tale of modern Kenya and the Kenya of the old days-- zamani --through the eyes of a family of legendary hunters. Chili Cavanaugh, a native of Oklahoma, was the first American to “enter the insular society of the big-game hunters” soon after World War I. His two sons, Coke and Lucien, born in Africa, do their wild father proud by rejecting the discipline of the British schools and running away to join him on safari. The three become known as much for their reckless courage on the hunt--their trademark is to wait until the last possible moment before pulling the trigger--as for their epic womanizing. Their relationship is based on constant competition; between them, they have divided up the range of possible masculine proficiencies, from whiskey drinking and card tricks to opening lines with women.

When the story opens, Lucien Cavanaugh is an aging bachelor. He is restless: dissatisfied with the outfitting business he has been running since big-game hunting was outlawed, tired of his solitude and perplexed by the forces--mainly entanglements with women--that drove his father, brother and him apart. In Nairobi he meets a woman doctor, Trey, who is fetching supplies for the refugee camp she tends on the northern border. On an impulse, he decides to drive her to the camp. As they drive, he attempts an explanation of how he fell out with his father and brother. “Maybe it was the times,” he explains. “When the hunting ended, all the old hunters got out of sorts.”

At the camp, they discover that a marauding leopard has been attacking and carrying off refugees. Big cats who develop a taste for human flesh must be destroyed, so Lucien invites his father and brother up to take part in a rare condoned hunt. “Three Hunters” weaves together the tale of the hunt and Lucien’s musings on what went wrong in the family.

This is a novel of restless men and the bonds between them, a terrific adventure story as well as a profound meditation on the intoxication of risk-taking.