The influence of the relative and absolute size of contestants on the agonistic behaviour of velvet swimming crabs was investigated. The agonistic interactions conformed to some of the general predictions from theoretical models of assessment strategy during contests. Crabs usually defeated smaller individuals and the duration and intensity of interactions were inversely related to the size difference between opponents. However, although the intensity of acts tended to increase during the early part of an inter- action, there was usually not a progressive escalation, and resolution of interactions was not always preceded by the most intense acts. In addition, following the initial displays, some smaller individuals continued offensively against opponents whose greater size they could probably detect. Information about the size discrimination ofNecora puber is lacking, but it appears that a perceived size difference may not always be used to resolve interactions conventionally. In natural populations of these crabs, there may not be a close relationship between size and fighting ability and this may promote more direct assessment of factorssuch as strength, endurance or motivation. The absolute size of contestants influenced the duration, but not the behavioural content of agonistic interactions. Crabs of large absolute size tended to resolve interactions in less time than small crabs. © 1993 The Association for the Study of Animal Behaviour.