American lobsters, Homarus americanus, form stable dominance relationships in captivity. Size, sex and stage in the moult cycle are important determinants for dominance. Other factors, such as recent agonistic experience play a role. This paper investigates how lobsters maintain their stable dominance relationships: they may recognize individuals or alternatively, recognize overall dominance status. We paired lobsters in two consecutive 'boxing matches'. Results indicate that lobsters remember familiar opponents when kept either in isolation or in communal tanks for 24 h between their first and second fights. Subordinates immediately backed away from familiar dominants, avoiding a second fight. In some animals, this memory lasted between 1-2 weeks if pairs were kept separate between the first and second fights. When paired for the second fight against unfamiliar dominant lobsters, subordinate lobsters from first fights actively fought and won the encounter. These results suggest that lobsters are capable of 'individual recognition'. In nature, the observed social organization of lobsters may be maintained by individual recognition of a small number of residents inhabiting separate, nearby shelters. (c) 1998 The Association for the Study of Animal Behaviour.