The article discusses approaches to crisis management based on the resources of political influence. The research is based on a dynamic model of resources of political influence, which includes the main resources of trust and competence, which, in turn, allow mobilizing and optimal distributing of material resources. The importance of resources of political influence in various aspects and at various stages of crisis management and anti-crisis communications has been demonstrated. On the basis of a systematic approach to the development of social systems, the features of the processes of substitution and compensation of resources in the conditions of crisis dynamics of the system are analyzed. Possibilities of concentration of power resources in crisis conditions are considered. The perspective of modern approaches to public management based on information, data and knowledge management and based on social intelligence is revealed. The study was conducted on the material of individual nuclear cities during the first wave of the spread of the new coronavirus infection.