This paper examines the set of equilibria and asymptotic stability of a large class of dynamical networks with nonidentical nonlinear node dynamics. The interconnection dynamics are defined by M-matrices. An example of such a class of systems include nonlinear consensus protocols as well as other distributed protocols of interest in cooperative control and distributed decision-making. We discuss the model’s relationship to the network topology, investigate the properties of its equilibria, and provide conditions for convergence to the set of equilibria. We also provide examples of the versatility of this model in the context of a sensor coverage problem. The model is extended to incorporate additional nonlinearities; an application for this latter model is also provided in the realm of neural networks.