This paper considers interconnected retarded nonlinear systems. Integral input-to-state stable subsystems and the construction of LyapunovKrasovskii functionals for their interconnections are focused on. Both discrete and distributed time-delays in the subsystems and the communication channels are covered. This paper provides a sufficient small-gain type condition for the stability of the interconnected systems with respect to external inputs in the framework of LyapunovKrasovskii functionals. Global asymptotic stability is addressed as a special case which deals with time-varying delays in communication channels effectively.