Abstract: We performed experiments with cichlid fish to test whether several basic aspects of dominance were the same in isolated pairs as in pairs within a social group of three or four. We found that the social context, whether a pair was isolated or within a group, strongly affected the basic properties of dominance relationships. In particular, the stability of relationships over time, the replication of relationships in successive meetings, and the extent of the loser effect were all significantly less in socially embedded pairs than in isolated pairs. We found no significant winner effect in either isolated or socially embedded pairs. These findings call into question many current approaches to dominance that do not consider social context as an important factor in dominance behavior. These findings also cast serious doubt on the validity of empirical and theoretical approaches based on dyadic interactions. Among these approaches are game theoretic models for the evolution of aggressive behavior, experimental designs evaluating how asymmetries in attributes influence the outcome of dominance