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Existing code update protocols for reprogramming nodes in a sensor network are either unsuitable or inefficient when used in a mobile environment. The prohibitive factor of uncertainty about a node's location due to their continuous movement coupled with the obvious constraint of a node's limited resources, pose daunting challenges to the design of an effective code dissemination protocol for mobile sensor networks. In this paper, we propose ReMo, an energy-efficient, multihop reprogramming protocol for mobile sensor networks. Without making any assumptions on the location of nodes, ReMo uses the LQI and RSSI measurements of received packets to estimate link qualities and relative distances with neighbors in order to select the best node for code exchange. The protocol is based on a probabilistic broadcast paradigm with the mobile nodes smoothly modifying their advertisement transmission rates based on the dynamic changes in network density, thereby saving valuable energy. Contrary to previous protocols, ReMo downloads pages regardless of their order, thus, exploiting the mobility of the nodes and facilitating a fast transfer of the code. Our simulation results show significant improvement in reprogramming time and number of message transmissions over other existing protocols under different settings of network mobility. Our implementation results of ReMo on a testbed of SunSPOTs also showcase its better performance than existing reprogramming protocols in terms of transfer time and number of message transmissions.