The consideration of inner, "intime" part of conviction forming process is offered. The latter are shown to be special personal formations possessing of own psychological structure. The problem of psychological foundation for them as well as the problem of cognitive and necessity-personality components interrelation is considered. It is shown that support on child's own potential and on inner logics of child's development is the necessary condition for conviction forming process effectiveness' increase. The thesis of morality's leading role in convictions of different kinds forming is substantiated. The task of working out of general strategy for conviction forming as a system of moral education for all stages of human development is considered.