Plenary session Stability analysis for nonlinear complex and hybrid systems Abstract. The paper deals with the stability problem of solutions of nonlinear dynamical systems with complex and changing structure of connections. The main results of stability analysis by means of nonlinear approximation are presented. Important aspects of the application of the theory of differential inequalities and the method of comparison to the solving of stability problem are described. The question of construction of auxiliary comparison systems for the considered dynamical systems is investigated. Stability criteria for these comparison systems are formulated. Methods of decomposition and aggregation of complex systems are studied. The effect of switching on stability is estimated. Some directions of development of classical results, relevant in recent years, are shown. In particular, it describes the application of these results to the solving of the absolute stability problem, to the modeling of population interactions in biological communities, to the stability analysis of the equilibrium positions of mechanical systems.