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Underwater wireless sensor networks (UWSNs) pose many challenges due to the intrinsic properties of underwater environments such as large propagation delays, node mobility and limited bandwidth capacity of acoustic channels. In this paper we present DUCS (distributed underwater clustering scheme), a new GPS-free routing protocol for UWSNs that does not use flooding techniques, minimizes the proactive routing message exchange and uses data aggregation to eliminate redundant information. Besides, DUCS assumes random node mobility and compensates the high propagation delays of the underwater medium using a continually adjusted timing advance combined with guard time values to minimize data loss and maintain communication quality. The simulations carried out demonstrate the effectiveness of the proposed scheme.