Zebras at the world- famous San Diego zoo. Zebras are social herd animals, for the most part, living in family groups with a stallion, several mares, and their offspring. During certain times of the year, these groups gather together to form loosely associated herds of up to several hundred, but the family groups still stay together within these larger groups. Most zebras are considered nomadic, without specific territories. The exception is the Grevy's zebra Equus grevyi. Stallions of this species mark out territories with urine and dung.