The evolutionary stability of the female-biased sex ratio observed in the wood lemming (Myopus schisticolor) is discussed. The hypothesis analysed is that the skewed sex ratio is maintained as a result of partial and/or recurrent inbreeding. Fredga et al. (1976, 1977) have suggested that an X-linked mutant gene, X, affects the male-determining action of the Y chromosome, thus converting some XY individuals into females. By a mechanism of selective non-disjunction in the foetal ovary only X-carrying eggs are produced. In particular the stability of that genetic mechanism (or the X chromosome) is analysed by considering the introduction of a "suppressing" sex-linked mutant gene Y. Several deterministic simulation models assuming father-daughter and/or brother-sister matings have been developed and analysed. It is concluded that in the case of extremely strong inbreeding, the hypothesised genetic mechanism may, as a result, be evolutionarily stable. Interpreting field observations on microtine rodents in general it is concluded that only a few species are likely to experience such extreme cases of inbreeding. The wood lemming and the related collared lemming (Dicrostonyx troquatus), another case which seems to have XY-females, are likely to exhibit sufficiently strong inbreeding.