We present a survey of passerine birds designed to investigate the frequency with which sexual dimorphism in coloration or color pattern has evolved from monomorphism (or the converse). Based on the number of genera that have both a monomorphic and a dimorphic species, and the minimum number of changes inferred to have occurred between genera, the transition between dimorphism and monomorphism has occurred at least 150 times. Using the Sibley/Ahlquist phylogeny, we obtain maximum likelihood estimates of the probability that one state will be in the other after one million years of 0.01 to 0.02 (monomorphism to dimorphism) and 0.03 to 0.04 (dimorphism to monomorphism). The rate of transition from dimorphism to monomorphism appears to be higher than the converse, and there are more monomorphic than dimorphic species. We conclude that the transition between alternative states is not difficult, and that the evolution of sexual dimorphism, given appropriate selection pressures, is unlikely to be constrained.