JFK's policy in Africa - a revealing look at overlooked history; J.F.K.: Ordeal in Africa, by Richard H. Mahoney. New York: Oxford University Press. 338 pp. $17.95.

WHEN one thinks of foreign policy and John F. Kennedy, what comes to mind first is usually the Bay of Pigs crisis at the start of his administration, the Cuban missile crisis which came later, or the gradually increased American military commitment in Vietnam. Seldom is his involvement in Africa mentioned. Yet, this occupied a considerable part of his administration's time during extended periods and aroused much controversy.

Kennedy's policies in Africa make for interesting study, as they reveal a gradual shift in the President's mind as to the role the United States should play in the third world, particularly regarding the newly independent nations of Africa.

During his congressional and senatorial years, John Kennedy emerged as a strong believer in a US policy of support for these new nations. As an early supporter of independence and self-determination, he opposed continued French rule in Indochina and Algeria. Yet he was not really a liberal in foreign affairs in the sense in which that term was then applied. He was rather a hardheaded judge of what he thought was in the US national interest. He saw independence as an inevitable process and believed it was in the US interest to side with gradual change. This anticolonial stance gained him the acquaintance and sympathy of future African leaders such as Kwame Nkrumah and Ahmed Sekou Toure and brought him into the public eye for the first time.

A large part of the book concerns US involvement in the Congo (now Zaire) and the Kennedy administration's attempts to build a durable and effective government for that country based on moderate center groups. There are concluding chapters on Kennedy's relations with Nkrumah's Ghana and on the early years of the Angolan struggle to gain independence from Portugal. These are ancillary, however, and the author rightly judges the Kennedy administration's foreign policy effectiveness on its record in the Congo.

An examination of that record shows that Kennedy never tipped his hand until faced with the consequences of inaction. It also reveals a tendency to wait and see if problems would solve themselves and a willingness to try all feasible alternatives, even distasteful ones.

During his presidential years Kennedy gradually moved away from his position of generally supporting the new nations. This shift started with a hard but less-known lesson than that of the Bay of Pigs - the assassination of the Congolese leader Patrice Lumumba. The role of the US government in the Lumumba assassination is carefully examined, as is its policy in supporting the UN military contingent in the country and its stance toward the short-lived ''breakaway'' state of Katanga.

This was a confused period. Kennedy felt strongly that US credibility on the issue of support for decolonization was at stake. To create a stable government in the newly independent Congo he had to forge a coalition among groups which had serious and sometimes nearly irreconcilable disagreements. When this could not be done he was forced to support the more conservative, right-wing elements. And he had to do it without seeming to resist change in the eyes of the third world or putting undue strain on the NATO alliance, since several of its members , such as Belgium and Britain, did not share Kennedy's views on independence for the Congo.

In Angola, Kennedy's policy was different. Instead of trying to reinforce a moderate center coalition (which did not exist), he sought to pressure both sides in order to achieve an orderly transition toward independence and avert a colonial war and possible Soviet intervention. At first he believed that the US could have it both ways: that the country could rely on an unweakened NATO (then riven by Portuguese opposition to Angolan independence) to preserve its national security interests while continuing to be perceived by the third world as a supporter of independence for those still under colonial rule. Over the course of time he found that he had to choose between the two. He chose Portugal and a strong NATO.

Kennedy's African policy, as the author notes, shows him to have been a cautious leader, committing himself only little by little when events seemed to be beyond his ability to influence them. It also shows him as a man who knew what he wanted but was rarely sure how he could do it and who always left himself a way out if disaster struck. The author describes him as a ''decision maker ruled by a sense of his limitations but, as a diplomat, ready to take full advantage of his presidential powers.''

These traits served him better in the Congo than in Vietnam, where he followed a course of steadily increasing US troop commitments without ever deciding how far he would ultimately go in committing himself.

Summing up Kennedy's African policies, Mr. Mahoney concludes that they succeeded in doing what no other American president before or after him had done: establishing a common ground between the ideals of newly independent third-world nations and American self-interest in the midst of a cold war-no mean achievement.