Sex-linked meiotic drive is found in a broad variety of taxa, including insects, birds, and mammals. In populations of some species, we see four types of sex chromosomes segregating: normal and driving X chromosomes and susceptible and resistant Y chromosomes. A theoretical analysis shows that a stable four-chromosome equilibria is a more common outcome in these systems than previously recognized. Cycling of sex chromosome frequencies and associated changes in the sex ratio are other predicted outcomes. The absence of cycling in nature may be due to migration among populations.