In this paper, we study dynamical networks consisting of neutral subsystems and propose a method that enables us to verify their stability and robustness with respect to time delays and disturbances. Time-delays are allowed not only to reside in both subsystems and interconnection channels in either of discrete and distributed forms, but also to appear in the neutral form. Each neutral subsystem is assumed to have a sort of integral input-to-state stable property. No assumption is made on the interconnection topology. A small- gain-type sufficient condition for global asymptotic stability and robustness of the network is developed and a Lyapunov- Krasovskii functional proving the stability is constructed.