We consider the synchronization problem for a class of directed networks where the agents receive relative output information from their neighbors, but lack independent information about their own state or output (they are non-introspective) and are unable to exchange internal controller states with their neighbors. We consider three classes of networks defined by the properties of the agent dynamics: homogeneous networks, where the agents are governed by identical linear models; heterogeneous networks, where the agents are governed by non-identical linear models; and networks with nonlinear and time-varying agent dynamics. In each case, the linear part of the dynamics is assumed to be minimum-phase. Our approach is based on a combination of low-gain and high-gain design techniques. (C) 2015 Elsevier Ltd. All rights reserved.