Dynamics of complex networked systems consisting of a large number of interconnected components (agents) has attracted considerable attention of researchers in control theory and dynamical systems. One of the most interesting questions in this area concerns the emergence of a coherent joint behavior of nodes caused by couplings between them, such as, e.g., their synchronization. We study a network where each node is a linear dynamical system of arbitrary order in discrete time, and couplings between the nodes are nonlinear and unknown but satisfy the sector inequality with known bounds. We obtain frequency-domain criteria of synchronization and stability of the network, which are generalizations of the Tsypkin criterion and the Jury–Lee criterion for discrete-time Lurie systems.