In this study, we present for the first time a model for the social structure of Risso’s dolphins (Grampus griseus Cuvier, 1812). Over the period 2004–2006, 1028 Risso’s dolphins were identified at Pico island, Azores. Individuals sighted on 10 or more occasions were included in the analysis of social structure (n = 183). High resighting rates indicate strong site fidelity for at least part of the population. We found that individuals form stable, long-term bonds organised in pairs or in clusters of 3–12 individuals. Social structure is stratified based on age and sex classes, with strong associations between adult males and between adult females. We suggest that clusters form the basic units of Risso’s dolphin society. Thirteen pods consisting solely of adults, likely males, and 3 pods consisting of mother–calf pairs were identified. Males are organised in stable, long-term associations of varying size that occur throughout the complete range of behavioural states observed. For females, associations can be of similar strength, but the time scale may vary depending on the presence of nursing calves. As subadults, associations also occur (pair formation), but are less stable than those observed for adults. We propose a new model for Risso’s dolphin societies known as a stratified social organisation, which differs from the fission–fusion and matrilineal society models.