I describe an integrative social-evolutionary model for the adaptive significance of the human oxytocinergic system. The model is based on a role for this hormone in the generation and maintenance of social familiarity and affiliation across five homologous, functionally similar, and sequentially co-opted contexts: mothers with offspring, female and male mates, kin groups, individuals with reciprocity partners, and individuals within cooperating and competing social groups defined by culture. In each situation, oxytocin motivates, mediates and rewards the cognitive and behavioural processes that underlie the formation and dynamics of a more or less stable social group, and promotes a relationship between two or more individuals. Such relationships may be positive (eliciting neurological reward, reducing anxiety and thus indicating fitness-enhancing effects), or negative (increasing anxiety and distress, and thus motivating attempts to alleviate a problematic, fitness-reducing social situation). I also present evidence that testosterone exhibits opposite effects from oxytocin on diverse aspects of cognition and behaviour, most generally by favouring self-oriented, asocial and antisocial behaviours. I apply this model for effects of oxytocin and testosterone to understanding human psychological disorders centrally involving social behaviour. Reduced oxytocin and higher testosterone levels have been associated with under-developed social cognition, especially in autism. By contrast, some combination of oxytocin increased above normal levels, and lower testosterone, has been reported in a notable number of studies of schizophrenia, bipolar disorder and depression, and, in some cases, higher oxytocin involves maladaptively 'hyper-developed' social cognition in these conditions. This pattern of findings suggests that human social cognition and behaviour are structured, in part, by joint and opposing effects of oxytocin and testosterone, and that extremes of such joint effects partially mediate risks and phenotypes of autism and psychotic-affective conditions. These considerations have direct implications for the development of therapies for alleviating disorders of social cognition, and for understanding how such disorders are associated with the evolution of human cognitive-affective architecture.