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In this paper a distributed clock synchronization algorithm is proposed. The algorithm requires asymmetric gossip communications between the nodes of the network, and is based on an PI-like consensus protocol where the proportional part compensates the different clock speeds while the integral part eliminates the different clock offsets. Convergence of the algorithm is proved and analyzed with respect to the controller parameter, when the underlying graph is the complete graph. Simulations results show the effectiveness of the proposed strategy also for more general communication topologies.