Introduction. The urgency of studying of the problems of correlation of chaotic dynamics and Genesis of socio-economic systems of the national research University is conditioned by the strengthening of innovative orientation of national economic development. Theoretical analysis. The article discusses the new socio-economic system of the type of national research universities. They represent the reaction of systemic changes and changes in the world economic environment, focused on knowledge and innovation. The paper formulates the features of such systems; positive consequences from them at different levels of economic development. The article analyzes the position of the national research universities on some indices of efficiency of their activity. Results. National research University it is a complex, open to external influences, dynamically and nonequilibrium nonlinear socio-economic system. It consists of a large number of interacting elements. The stationary state of such a system is unstable. The system responds flexibly to requests from the economy. It provides increase of competitiveness of the Russian education and science, staffing of the basic sectors of the innovation economy, commercialization of scientific research. Such a system should be managed by controlled chaos feedback in order to stabilize their own chaotic behavior. Correlation of chaotic dynamics and development of socio-economic systems of the national research University allows to make a conclusion about how the interaction of the natural and rational started these processes, and about the interdependence and interaction between them.