The paper contains evidence that within a traditional concept of altruism representations of two essentially different types of non-egoistic aims and behaviors are not differentiated. The first type supposes a general humanistic aim to help other people without their special differentiation. The second type supposes that a subject while ignoring his own interests helps another subject in a particular way — by doing damage to his rivals. The concept «alternative altruism», or «alter-altruism» is proposed for the latter type of attitude and behavior. The classification of different human activities in a three-dimensional space «cooperation-counteraction-execution/ reflection» is presented. Manifestations of alter-altruism towards «enemies» and «allies» are being described. Moral dilemmas of alter-altruistic activities are discussed and future research aims are set.