Understanding why animal societies take on the form that they do has benefited from insights gained by applying social network analysis to patterns of individual associations. Such analyses typically aggregate data over long time periods even though most selective forces that shape sociality have strong temporal elements. By explicitly incorporating the temporal signal in social interaction data we re-examine the network dynamics of the social systems of the evolutionarily closely-related Grevy's zebras and wild asses that show broadly similar social organizations. By identifying dynamic communities, previously hidden differences emerge: Grevy's zebras show more modularity than wild asses and in wild asses most communities consist of solitary individuals; and in Grevy's zebras, lactating females show a greater propensity to switch communities than non-lactating females and males. Both patterns were missed by static network analyses and in general, adding a temporal dimension provides insights into differences associated with the size and persistence of communities as well as the frequency and synchrony of their formation. Dynamic network analysis provides insights into the functional significance of these social differences and highlights the way dynamic community analysis can be applied to other species.