Structured peer to peer (P2P) systems organize a large number of nodes in well-defined structures and provide efficient and scalable search functionalities. They have been used as a basis to implement many network services and applications. As more and more computers have wireless connections and can move from one place to another, supporting mobility in the structured P2P systems becomes an important issue. In this paper, we present an algorithm called Range based Updating AlgorithM (RUAM) to efficiently support mobile nodes in structured P2P systems. RUAM allows a mobile node to actively update information stored in other nodes when it changes its address. Hence, the outdated routing information in the system can be greatly decreased. The simulation results show that RUAM is efficient in updating stale states caused by mobile nodes and greatly improves the lookup performance.