Full text can be accessed at http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2028.1988.tb01124.x/fullBetween 1970 and 1980 the population size of the migratory zebra in the Serengeti remained constant. During the same period the population of wildebeest, also a large migratory ungulate, increased in a manner compatible with existing ecological theories. Sinclair & Norton-Griffiths (1982) have produced evidence to suggest that predation pressure was the factor that prevented the zebra population from increasing. This paper presents further evidence, based on population structure, which shows that the size of zebra population should have increased.