The right hemisphere plays a crucial role in social processing. Human mothers show a robust left cradling/holding bias providing greater right-hemispheric involvement in the exchange of social information between mother and infant. Here, we demonstrate that a similar bias is evident in face-to-face spatial interactions in marine and terrestrial non-primate mammals.Walruses and Indian flying foxes showed a significant population-level preference for the position which facilitates the use of the left visual field in both mother and infant. This behavioural lateralization may have emerged owing to benefits conferred by the enhanced right-hemispheric social processing providing the mother and infant an optimal perception of each other.