Social relationships between group members are a key feature of many animal societies. The quality of social relationships has been described by three main components: value, compatibility and security, based on the benefits, tenure and stability of social exchanges. We aimed to analyse whether this three component structure could be used to describe the quality of social relationships in wild Barbary macaques (Macaca sylvanus). Moreover, we examined whether relationship quality was affected by the sex, age and rank differences between social partners, and investigated the asymmetric nature of social relationships. We collected over 1,900 hours of focal data on seven behavioural variables measuring relationship quality, and used principal component analysis to investigate how these variables clustered together. We found that relationship quality in wild Barbary macaques can be described by a three component structure that represents the value, compatibility and security of a relationship. Female-female dyads had more valuable relationships and same-age dyads more compatible relationships than any other dyad. Rank difference had no effect on the quality of a social relationship. Finally, we found a high degree of asymmetry in how members of a dyad exchange social behaviour. We argue that the asymmetry of social relationships should be taken into account when exploring the pattern and function of social behaviour in animal societies.