This note addresses the problem of synchronization for general dynamical networks with nonidentical nodes. The coupling strength, outer coupling configuration and inner connection in such networks are all time varying. Neither an equilibrium for each node nor a synchronization manifold is assumed to exist. An estimate of the convergence domain for a general class of time-varying nonlinear systems is given. By introducing the average dynamics of all nodes and based on this estimate, a criterion of global synchronization in the sense of boundedness of the maximum state deviation between nodes is developed. An explicit bound of the maximum state deviation between nodes is obtained by the maximum difference between each node dynamics and the average dynamics. The proposed criterion is an extension of several related synchronization criteria for the case of identical nodes to the case of nonidentical nodes.