I present game theory models for parental care by male and female parents of male and female offspring. The models include the effects of Fisherian frequency dependence (FFD), the trade-off between offspring fitness and the residual fitness of the parent, and the conflict between the two parents. The models are used to make predictions about the factors selecting for biases in parental care with respect to either offspring or parental sex. The models predict that: (1) male and female offspring will receive different amounts of care when the offspring functions (relating fitness accrued through an offspring to the amount of care that it receives, excluding the effects of FFD) differ between the male and female offspring; (2) male and female parents will give different amounts of care when either (a) the parental functions (relating the loss in residual fitness to the total amount of care given by the parent, excluding the effects of FFD) differ between male and female parents, or (b) offspring functions differ between male and female offspring and FFD also acts on residual fitness of parents; and (3) there will be an interaction between offspring and parental sex on the amount of care received (a) by an offspring within a family when the offspring functions are not the same for male and female parents (but then the sex bias is extreme and one parent does not care for one sex of offspring), and (b) by the family in relation to its sex ratio when offspring functions differ between male and female offspring (but not necessarily between male and female parents) and parental functions differ between male and female parents. Copyright 1998 The Association for the Study of Animal Behaviour