The study covers results of theoretical analysis of the basic contradiction within intergenerational interactions in the network society, defined by the fact that modern children live in the system of «horizontal» network relations, in the format of network societies, and adults are guided by the developed «vertical» models of relations and social behaviour. Self-organization is defined as an unapproved process of formation of small informal societies (groups, associations, formations, societies, teams) which factor-impulse being their source. The essence of self-organization is effective joint interactions aimed at achieving certain goals, which have arisen as a reflexion of the factor-impulse; the existence basis of self-organization is social interactions or interpersonal communication. The factor-impulse is an idea, subject, phenomenon, event, information, or provocation which generate interest in one person or a group of people «launches» the process of self-organization. The most effective type of activity of the adult under the conditions of self-organization of children is pedagogical support which is aimed at the development of the child’s readiness to build the individual life project independently, and in the adult’s readiness to react adequately to problem situations arising at children at various social institutes.