Abstract A few mammals have unusual sex determining systems whereby fertile XY females live alongside XX females and XY males. These systems are regarded as evolutionary paradoxes because of the production of sex-reversed individuals and non-viable embryos, but they nevertheless seem stable over evolutionary time. Several hypotheses have been proposed to account for their stability, including models involving sex chromosome drive ( i . e ., biased transmission of sex chromosomes to the next generation). Here we corroborate this hypothesis in Mus minutoides , a close relative of the house mouse in which the presence of XY females is due to the evolution of a third sex chromosome: a feminizing X. Through extensive molecular sexing of pups at weaning, we reveal the existence of a remarkable male sex chromosome drive system in this species, whereby direction and strength of drive is conditional upon the genotype of males’ partners: males transmit their Y to almost 80% of their offspring when mating with XX females, and only 36% when mating with XY females. Using mathematical modelling, we explore the joint evolution of these unusual sex-determining and drive systems, revealing that different sequences of events could have led to the evolution of this bizarre system, and that the “conditional” nature of sex chromosome drive stabilizes the feminizing X, and even precludes a return to a standard XX/XY system.