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We propose an approach to analyze the resilience to failures of structured P2P systems. The approach is Markov-chain based, and can be applied to systems with relatively stable size and uniformly distributed nodes. We apply our method to several well-known structured P2P systems. We find that finger neighbors and special neighbors have different influences on the resilience features of P2P systems. More particularly, finger neighbors have significant influence on the average path length while special neighbors influence the hit ratio. Following the above observation, we propose to add some finger neighbor(s) to nodes of the CAN (content-addressable network) system which originally have no such finger neighbor(s). We use the small-world phenomenon to form the CAN-small-world (CAN-SW) system. We then apply the proposed Markov-chain based approach to analyze its resilience. We find that the performance of the system under failures or not, has been improved significantly, particularly, in terms of the average path length.