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We consider the problem of supporting continuous spatial queries in a new and challenging network environment, namely a Mobile Peer-To-Peer (MP2P) network. Specifically, we propose a distributed technique, called ExtRange, that can efficiently answer continuous moving range queries in a MP2P network. The two key ideas in ExtRange are extended range and safe period. For each query, ExtRange extends the query monitoring region beyond the query range to ensure the accuracy of the query result under the dynamic condition of mobile nodes. Additionally, for each query it monitors, a mobile node computesa safe period, during which the mobile node does not have to update its location with the query node. Through analytical study, we prove that ExtRange guarantees the accuracy for query results when network communication is perfect. Using extensive simulation study, we show that ExtRange delivers high accuracy for query results with low associated costs under realistic simulation settings.