The stability analysis is developed for nonlinear dynamical systems. Conditions which guarantie the stability of an equilibrium point of a system are derived by using Lyapunov's method. Next the absolute stability of feedback systems is studied : this problem is concerned with the stability analysis of a linear system for a class of nonlinear feedbacks which satisfy a given sector condition. Two criteria are developed : the circle and Popov criteria, that guarantie absolute stability in terms of strictly positive real transfer matrices. Finally two illustrative examples are studied, in order to show how these criteria can be used in applications.