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Existing position-based unicast routing algorithms which forward packets in the geographic direction of the destination require that the forwarding node knows the positions of all neighbors in its transmission range. This information on direct neighbors is gained by observing beacon messages each node sends out periodically. Due to mobility, the information that a node receives about its neighbors becomes outdated, leading either to a significant decrease in the packet delivery rate or to a steep increase in load on the wireless channel as node mobility increases. In this paper, we propose a mechanism to perform position-based unicast forwarding without the help of beacons. In our contention-based forwarding scheme (CBF) the next hop is selected through a distributed contention process based on the actual positions of all current neighbors. For the contention process, CBF makes use of biased timers. To avoid packet duplication, the first node that is selected suppresses the selection of further nodes. We propose three suppression strategies which vary with respect to forwarding efficiency and suppression characteristics. We analyze the behavior of CBF with all three suppression strategies and compare it to an existing greedy position-based routing approach by means of simulation with ns-2. Our results show that CBF significantly reduces the load on the wireless channel required to achieve a specific delivery rate compared to the load a beacon-based greedy forwarding strategy generates.