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In this paper, we propose a framework to establish localization and routing in mobile underwater sensor networks. Localization and routing are done at two consecutive rounds. Localization messages include localization specific data and additional fields which are used in the routing decision. The proposed "catch up or pass" forwarding algorithm is a greedy geo-forwarding scheme. It benefits from the uncontrolled motion of the underwater nodes. The underwater nodes use position and velocity information to decide whether to carry the packet until they "catch up" with a sink or "pass" it to a faster or slower relay.