We examine the necessary conditions for the spread of genes that determine ‘selfish’ and ‘cheating’ behaviors and the rate of spread of these genes through structured populations, in order to address the question of the invadability of altruistic systems by ‘anti-social’ mutations. We find that, although ‘cheaters’ always have a higher relative fitness than altruists within groups, population structures which permit the evolution of altruism also preclude invasion by anti-social mutations. These results are related to a discussion by Hamilton (1971) concerning the limits to the evolution of altruistic and selfish behaviors.