Abstract: There are two distinct types of social organization and, accordingly, two types of mating systems in equids. In the horse, Plains zebra and Mountain zebra, the adults live in non-territorial and cohesive one-male groups and in stallion groups. The family stallions have exclusive mating rights which are respected by all others. In Grevy's zebra and in the African and Asiatic wild asses, the stallions are permanently territorial and have exclusive mating rights within their territories. Ecological and evolutionary aspects are discussed.