Sexually selected feticide—the death of infants in utero as a result of male behaviour—has only rarely been described or analysed, although it is presumed to be favoured by the same selective pressures that favour sexually selected infanticide. To test this hypothesis, we measured the frequency of feticide and infanticide by male baboons of the Amboseli basin in Kenya, and examined which characteristics of a male and his environment made him more likely to commit feticide and/or infanticide. We found a dramatic increase in fetal and infant death rates, but no increase in death rates of 1- to 2-year-old individuals, following the immigration of males who stood to benefit from feticide and infanticide. Specifically, fetal and infant death rates were highest following immigrations in which: (i) the immigrant male rapidly attained high rank, (ii) that male remained consistently resident in the group for at least three months, (iii) food availability and social group range overlap was relatively low and (iv) relatively many pregnant females and/or dependent infants were present. Together, these results provide strong evidence for the existence of both sexually selected feticide and infanticide in our population, and they indicate that feticide and infanticide are conditional male behavioural strategies employed under particular circumstances.