Sufficient conditions for the Lyapunov stability of several classes of (a) continuous-time composite systems described by ordinary differential equations, (b) discrete-time composite systems described by difference equations, (c) sampled-data composite systems, and (d) composite systems described by functional differential equations are established. In all cases the objective is the same: to analyze the stability of large-scale composite systems in terms of their lower order subsystems and in terms of their interconnecting structure.In order to demonstrate the usefulness of the present approach, several specific examples are considered.