Cords and Aureli (2000) proposed that relationship quality can be described by three components, i.e., value, security, and compatibility, based on the benefits social partners receive from their relationship and on how likely it is for them to maintain a stable friendly relationship over time. We aimed to examine whether this 3-components structure can describe social relationships and to investigate the degree of asymmetry of social relationships. We used the Japanese macaque as our model species, as group members may form strong social relationships with one another. We collected 359.2 h of focal samples, on 21 monkeys, and ran a principal component analysis (PCA) on dyadic scores for 9 variables measuring social relationships, e.g., grooming or aggression. This PCA gave 3 components. However, a second PCA run on scores per individual, i.e. for each variable and dyad we obtained 1 score for the actor and 1 for the receiver of behavior, gave a 5-component structure. We interpreted this result as evidence of the asymmetric nature of social relationships, in terms of the frequency and type of behavior exchanged between social partners, in the Japanese macaque. This interpretation was confirmed by the low correlation coefficients between behaviors given and received within a dyad. Overall these results provide mixed support for the 3-components structure predicted by Cords and Aureli (2000). They also show that social relationships may be largely asymmetric and that this asymmetry should be considered in studies on social behavior.