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This paper addresses the problem of synchronizing networks of nonidentical, nonlinear dynamical systems described by Euler-Lagrange equations, which are assumed fully-actuated, with their states available for measurement, but with unknown parameters. The only assumption made on the communication graph is that it is connected. Moreover, the communication is subject to constant time delays, which are also unknown. The main result of the paper is the construction of an adaptive controller that achieves global full-state synchronization, i.e., the difference between the agents positions and velocities asymptotically converges to zero. If a desired trajectory for all systems is given, a slight modification to the proposed scheme achieves also full-state synchronization. Simulations using a ten robot manipulator network are used to illustrate the performance of the proposed schemes.