Head: long and narrow, especially the muzzle, which has a brown spot separated from the striped pattern by a white area. Large rounded ears, with a black edge and a white tip. The inner margin is framed by a hairy fringe.

The basic social unit is a female with her 1-2 younger foals. These families combine in groups of 5-10 females with their offspring, but they are unstable unions, without cohesion or rank hierarchies. Groups may associate with plains zebras and several antelope species, and during the dry season they can aggregate in mixed herds of 100-200 head, sometimes reaching 450. These herds migrate in the dry season in search of rich water and pasture areas, but afterwards they disperse to avoid competing for the scarce grass.

Adult males are solitary and territorial. Generally they dominate an area of 6 km², bordered by topographic accidents such as stream beds. Stallions signpost their domains with urine and dung piles, apart from raising awareness with their physical presence and their call, a blend of an ass's bray and a hippopotamus's growl. In many cases and if conditions of water and food are favourable, territorial males will remain in their domains all year round without joining the migrations, thus awaiting for the return of females with the onset of rains, when the peak breeding season begins. Neighbouring territorial males frequently socialize at the boundaries through a series of rituals, and combats may sometimes break out, in which males neck-wrestle, bite each other and exchange kicks.

The groups of mares usually roam through overlapping territories, covering each day a distance of 10-15 km that comprises the domains of several territorial males. At the age of 3, young males leave their mothers to gather in bachelor groups of 2-6, maximum 10. These groups can be allowed by territorial stallions into their domains, and they may even mix up with female groups in search of pasture, but only as long as mares are not in heat. If estrous females are present, the adult stallion will never tolerate an invasion by another territorial male, but it may grant the presence of bachelor groups within its territory as long as they keep at a reasonable distance from estrous mares. At the age of 6, young bachelors can demarcate their own territory.

The primary predator of Grevy's zebra is the lion, that preys both on adults and foals. The latter are threatened as well by leopards and hyenas. During drought, when females are bound to walk great distances in search of water, they often leave foals unattended. The youngs lack concealment instinct and thus become easy prey for carnivores. The longevity of Grevy's zebras is 15-20 years.

It is remarkable that, regardless of the stripes and the name of "zebra" shared by both, actually Grevy's and plains zebras are not more closely related than each of them is with horses or asses. This is also shown by their different social organizations, which respond to adaptations to diverse habitats. Plains zebras are basically nomadic and non-territorial, hence stallions find it convenient to join the groups of mares and follow them along their movements to ensure reproduction. Instead, Grevy's are territorial despite their migrations, so males can establish their domains and thus gain access to females in transit through their territory.