The author analyses the fundamental issues of the crisis of economic science and develops a new scientific paradigm that can explain many anomalous facts, which do not fit the «mainstream» of economic thought. The reasons for the inability of the latter to explain the observed crises and processes of modern economic development rooted in the inadequacy of the basic assumptions of neoclassical economic theory are revealed. Its (neoclassical economic theory) concentration on the study of the position of market equilibrium, which is never achieved in the real economy, leads to scholastic interpretations of the processes of distribution of the public product. These interpretations are degenerated in the apology of the existing order of regulation of the economy. The proposed new approach is focused on the study of issues of economic development, and the changes in the economic system are the main subject of the analysis. The author pays attention to the fact that the dynamics of these changes in general case is nonlinear, nonequilibrium and uncertain. The patterns of economic dynamics due to the features of scientific-technical progress, technological life cycles and global economic structures, mechanisms of formation of technological trajectories and industrial cycles are revealed. The development of the modern economic system is represented as a movement from one attractor to another, which is never reached due to continuous emerging of innovations creating the new attractors. A new scientific paradigm explains the reasons for periodically occurring economic crises interrupting the process of economic growth, reveals the patterns of the latter, provides some justification for recommendations of successful economic policy.