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In this paper, the synchronization problem is investigated for a class of nonlinear delayed dynamical networks with heterogeneous impulsive effects. The intrinsic properties of heterogeneous impulses are that impulsive strengths are inhomogeneous in both time and space domains, i.e., the impulsive effect in each node is not only nonidentical from each other, but also time-varying at different impulsive instants. The purpose of the addressed problem is to derive synchronization criteria such that, the nonlinear delayed dynamical networks with heterogeneous impulses can be synchronized to a desired state. By means of a time-dependent Lyapunov function and the comparison principle, several sufficient conditions are established under which nonlinear dynamical networks with heterogeneous impulsive effects are exponentially synchronized to a desired state. An example is given to show the effectiveness of the proposed results.