MANY species exhibit colour polymorphisms associated with alternative male reproductive strategies, including territorial males and 'sneaker males' that behave and look like females1–3. The prevalence of multiple morphs is a challenge to evolutionary theory because a single strategy should prevail unless morphs have exactly equal fitness4,5 or a fitness advantage when rare6,7. We report here the application of an evolutionary stable strategy model to a three-morph mating system in the side-blotched lizard. Using parameter estimates from field data, the model predicted oscillations in morph frequency, and the frequencies of the three male morphs were found to oscillate over a six-year period in the field. The fitnesses of each morph relative to other morphs were non-transitive in that each morph could invade another morph when rare, but was itself invadable by another morph when common. Concordance between frequency-dependent selection and the among-year changes in morph fitnesses suggest that male interactions drive a dynamic 'rock–paper–scissors' game7.