An interaction between sex-linked inheritance and sex-biased mutation rates may affect the rate of adaptive evolution. Males have much higher mutation rates than females in several vertebrate and plant taxa. When evolutionary rates are limited by the supply of favorable new mutations, then genes will evolve faster when located on sex chromosomes that spend more time in males. For mutations with additive effects, Y-linked genes evolve fastest, followed by Z-linked genes, autosomal genes, X-linked genes, and finally W-linked and cytoplasmic genes. This ordering can change when mutations show dominance. The predicted differences in substitution rates may be detectable at the molecular level. Male-biased mutation could cause adaptive changes to accumulate more readily on certain kinds of chromosomes and favor animals with Z-W sex determination to have rapidly evolving male sexual displays.