Sexual selection arises when genetically different males show heritable differences in reproductive success. Mouse mating behaviour involves both male competition and female choice. In this paper we show that introduced Y-linked DNA markers spread more extensively through a natural population than do genes inherited matrilineally. Differences in mating success between the sexes and among individual males may alter the pattern and rate of gene flow in natural populations. Another interesting possibility is that the success of the introduced Y chromosome may be attributable to so-called `selfish' traits, such as sex-linked meiotic drive or intra-uterine competition. However, this study provides little unequivocal evidence to support this view. Differential success of introduced versus resident males may have implications for the reintroduction of endangered mammals into residual wild populations.