Female opossums produced a significantly greater number of male-biased than female-biased first litters and showed a trend for a greater number of female-biased than male-biased second litters. These results could not be predicted from existing sex ratio theories. Therefore, we propose a new explanation, the first-cohort advantage hypothesis: Females will increase their fitness by producing more males than females in their first than in their second litters when first-cohort males have a mating advantage over second-cohort males. On the average, larger male opossums achieve more matings than smaller males. First-cohort male opossums are larger than second-cohort males during their first year of reproduction; given high mortality rates, this may be their only year of reproduction. Therefore, females should have greater inclusive fitness by producing more males in their first than in their second litters of the year. Size does not influence female reproductive success to the same degree as in males, and thus, because of the small-male disadvantage and because of Fisher's rare-sex advantage hypothesis, females should produce more females than males in their second than in their first litters.