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Passivity-based control has emerged as an important paradigm for synchronization of networked robotic systems. Despite the practical utility of task-space algorithms, the previous results focused on joint-space synchronization and were primarily derived for kinematically identical manipulators. Hence, in this paper, the problem of task-space synchronization of (possibly redundant) heterogeneous robotic systems is studied. By exploiting passivity-based synchronization results that are developed previously, an adaptive control algorithm is proposed to guarantee task-space synchronization of networked robotic manipulators in the presence of dynamic uncertainties and time-varying communication delays. To demonstrate the efficacy of the proposed framework, numerical simulations and experiments are conducted with redundant and nonredundant manipulators, respectively.