Abstract--In this paper, a synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays. The complex networks addressed which include neural and social networks as special cases are quite general. Rather than the commonly used Lipschitz-type function, a more general sectorlike nonlinear function is employed to describe the nonlinearities existing in the network. The distributed infinite time delays in the discrete-time domain are first defined. By utilizing a novel Lyapunov