Abstract: A theoretical analysis is made of the evolution of behavioural strategies in contest situations. It is assumed that behaviour will evolve so as to maximize individual fitness. If so, a population will evolve an [`]evolutionarily stable strategy', or ESS, which can be defined as a strategy such that, if all members of a population adopt it, no [`]mutant' strategy can do better. A number of simple models of contest situations are analysed from this point of view. It is concluded that in [`]symmetric' contests the ESS is likely to be a [`]mixed' strategy; that is, either the population will be genetically polymorphic or individuals will be behaviourally variable. Most real contests are probably asymmetric, either in pay-off to the contestants, or in size or weapons, or in some [`]uncorrelated' fashion; i.e. in a fashion which does not substantially bias either the pay-offs or the likely outcome of an escalated contest. An example of an uncorrelated asymmetry is that between the [`]discoverer' of a resource and a [`]late-comer'. It is shown that the ESS in asymmetric contests will usually be to permit the asymmetric cue to settle the contest without escalation. Escalated contests will, however, occur if information to the contestants about the asymmetry is imperfect.