Social norms – rules governing which behaviours are deemed appropriate or inappropriate within a given community – are typically taken to be uniquely human. Recently, this position has been challenged by a number of philosophers, cognitive scientists, and ethologists, who have suggested that social norms may also be found in certain non‐human animal communities. Such claims have elicited considerable scepticism from norm cognition researchers, who doubt that any non‐human animals possess the psychological capacities necessary for normative cognition. However, there is little agreement among these researchers about what these psychological prerequisites are. This makes empirical study of animal social norms difficult, since it is not clear what we are looking for and thus what should count as behavioural evidence for the presence (or absence) of social norms in animals. To break this impasse, we offer an approach that moves beyond contested psychological criteria for social norms. This approach is inspired by the animal culture research program, which has made a similar shift away from heavily psychological definitions of ‘culture’ to become organised around a cluster of more empirically tractable concepts of culture. Here, we propose an analogous set of constructs built around the core notion of a normative regularity , which we define as a socially maintained pattern of behavioural conformity within a community . We suggest methods for studying potential normative regularities in wild and captive primates. We also discuss the broader scientific and philosophical implications of this research program with respect to questions of human uniqueness, animal welfare and conservation.