Social organization of pain zebras (Equus burchelli Gray, 1824) was studied in the Isiolo National Park in Kenya from June 1978 to June 1980. Their society is composed of one-male groups (consisting of one adult male, several adult females and their offspring) and all-male groups (consisting of full adult and young adult males). All the individuals which appeared in the study area were thoroughly identified throughout the study period, and the membership of each group was confirmed. The main data analyzed in the present paper are (a) moving range of the study groups and movements of nonresident groups, (b) group transfer of individuals during the two years, and (c) observation of behaviours in relations to the group transfer. Based on these analyses the cluster of several one-male groups and an all-male group living in the study area was concluded to be a social entity which is one level higher than a one-male group or an all-male group. Such social organization was compared with social organization of other species, especially with that of baboon species. Finally, it was noted that neighborhood relationship plays an important role for the formation of a two-layered social group such as the band in gelada baboons and the cluster in plain zebras.