The analysis of regularities of formation of solidary relations as a subsystem of an integral system of public relations together with an antipode – subsystem of conflict relations is presented. Solidary relations in society occupy a more significant, important place than conflicts. The history of research of solidary relations from Plato and Aristotle to modern researchers is shown. The detailed analysis of the ideas of P.A. Kropotkin as developer of bases of the complete concept of the solidary relations and new evolutionary theory is carried out. Incompleteness of these ideas which aren't brought to complete theoretical system, and their destiny as ignored and forgotten by social science are shown. Definition of the solidary relations formed through merge of personal interests with public, their transformation into uniform, general interest, into aspiration of everyone and all to a common goal, the benefit and harmony is given. The structure of solidary relations is described in terms of sources, formation prerequisites, subjects, time, degree of durability and spheres of activity is disclosed. On the basis of mature solidary relations, a solidary society will be formed, which is still in an unfinished state. The highest form of the solidary relations will be reached on the scale of all mankind as a result of globalization processes the scientific and practical tool for the implementation of which the concept of sustainable development nowadays acts. The internal contradictoriness of solidary relations, the prospects for the formation on their basis of a new social system are shown. The tasks of social scientists in creating a new theory of evolution are identified by combining the Darwinian concept of the struggle for existence with the idea of solidarity and collectivism, the development of metacivilization philosophy and the transcivilizational evolutionary theory.