Zanuck, a home-grown movie mogul; Zanuck: The Rise and Fall of Hollywood's Last Tycoon, by Leonard Mosely. Boston: Little, Brown & Co. 424 pp. $19.95.

Darryl F. Zanuck was part of a breed that doesn't exist anymore: the movie mogul. The moguls were ruthless businessmen who at the same time were among the world's greatest showmen. As production head of Twentieth Century-Fox, Zanuck was responsible for films like ''The Grapes of Wrath,'' ''How Green Was My Valley,'' and ''Gentleman's Agreement.''

Leonard Mosely's biography is a fascinating account of Zanuck's career, particularly in pointing out how Zanuck differed from his counterparts at the other studios. Zanuck was not an immigrant like Louis Mayer or Jack Warner, but a Nebraska boy. Also unlike other studio chiefs, he had the highest respect for the contribution of the screenwriters, and would brook no changes once he had approved the shooting script.

On the other hand, like others in positions of power in Hollywood in the '30s and '40s, Zanuck could be vulgar in both speech and action. Mosely gives full rein to this vulgarity, sometimes more than is necessary.

Zanuck's relations with women other than his wife, for example, undoubtedly had an effect on his life and his work, but Mosely occasionally steps over the line of illustrative anecdote and gives us gossip instead.

More unforgivable are the errors in the text. Typographical errors are bad enough, but when it states that Betty Grable was involved with ''Duel in the Sun'' or that the director of ''The Sound of Music'' was David (instead of Robert) Wise, this is evidence of either sloppiness of research or faulty memory.

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