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A key challenge in peer-to-peer computing systems is to provide a decentralized and yet reliable service on top of a network of loosely coupled, weakly connected and possibly unreliable peers. This paper presents an effective dynamic passive replication scheme designed to provide reliable service in PeerCQ, a decentralized and self-configurable peer-to-peer Internet information monitoring system. We first describe the design of a distributed replication scheme, which enables reliable processing of long-running information monitoring requests in an environment of inherently unreliable peers. Then we present an analytical model to discuss its fault tolerance properties. A set of initial experiments is reported, showing the feasibility and the effectiveness of the proposed approach.