Female kangaroos and perhaps other female marsupials have a unique form of dosage compensation for X-linked genes in their soma. In these animals the paternal X is inactive. Heterozygote females therefore have the phenotype of one or the other of the homozygotes, with the allele which is expressed coming from their mother. The unexpressed paternally derived allele may, however, be transmitted to the next generation in the usual Mendelian manner and there be expressed. Such a combination of haploid phenotypic expression and diploid genotypic behaviour on the part of X-linked genes in kangaroos makes their population genetics unique. This paper examines the possibilities for balancing selection in the kangaroo X chromosome system and shows that balanced polymorphisms are unlikely to occur. If 1 - a, 1, 1 - b and 1 are the selection coefficients of the alpha1 females, alpha2 females, alpha1 males and alpha2 males respectively (where alpha1 is the phenotype when A1 is expressed and alpha2 the phenotype when A2 is expressed), then the equilibrium is reached when the gene frequency of A1 in females = 0-5(a-1 + b-1), which takes values between 0 and 1 for only a few of the biologically likely values of a and b.