The concept of territoriality needs review in the light of recent mammalian studies. Intensive behavioural observations were carried out on the white rhinoceros in Zululand, South Africa, and results on social organisation are summarised. Territoriality is exhibited by certain adult males and has the following features: (i) mutually exclusive ranges of 1-2 km2; (ii) a dominant assertiveness in interactions within the territory; (iii) specialised scent marking techniques using dung and urine; (iv) exclusive participation in reproduction. Territories may be shared with one or more subsidiary bulls. Territoriality in the white rhino may be characterised as a space-correlated dominance relationship with the function of ordering reproductive competition among males. It plays no significant role in population regulation. These conclusions are extended to other territorial ungulates. Methodological criteria for territoriality are suggested. Evidence is needed on (i) differing social classes; (ii) range utilisation patterns; (iii) spatial features of dominance relationships