The article is devoted to highlighting the peculiarities of the evolutionary economy. The characteristic features of evolutionary changes in the economic system are highlighted. Emphasis is placed on the methodological principles of the development of complex systems. The position that the evolution of the economy and society is based on the laws of nonlinear development is substantiated. The peculiarities of the functioning of the modern economic system on the basis of instability and nonlinearity are revealed. It is emphasized that evolutionary economics is a relatively new direction of economic science, which considers economic processes as spontaneous, open, and irreversible, due to the interaction of external and internal factors. Signs of evolutionary economics from the standpoint of a nonlinear paradigm are also highlighted. The author proposes to study the evolution of the banking system from the standpoint of a nonlinear paradigm.