The social system stability under terrorist impacts is considered from the perspective of nonlinear dynamics of systems and deterministic chaos. The traits of social system dynamics and system stability are determined by the properties of potential functions, i.e. characteristic points on potential hyper surfaces, and by their distribution in configuration space, or by special points in the corresponding phase space. The possibility for the system subjected to minor disturbances to transit from the stable state into the chaos area where its further behavior is unpredictable is shown. The special states of social systems when the system can be withdrawn from the stable state by minor disturbance can now be determined by means of monitoring the system state, analysis of complex quantitative and qualitative indices of strategic risks, and Kondratiev cycles.