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The current peer-to-peer (P2P) content distribution systems are constricted by their simple on-demand content discovery mechanism. The utility of these systems can be greatly enhanced by incorporating two capabilities, namely a mechanism through which peers can register their long term interests with the network so that they can be continuously notified of new data items, and a means for the peers to advertise their contents. Although researchers have proposed a few unstructured overlay-based publish-subscribe systems that provide the above capabilities, most of these systems require intricate indexing and routing schemes, which not only make them highly complex but also render the overlay network less flexible toward transient peers. This paper argues that for many P2P applications, implementing full-fledged publish-subscribe systems is an overkill. For these applications, we study the alternate continuous query paradigm, which is a best-effort service providing the above two capabilities. We present a scalable and effective middleware, called CoQUOS, for supporting continuous queries in unstructured overlay networks. Besides being independent of the overlay topology, CoQUOS preserves the simplicity and flexibility of the unstructured P2P network. Our design of the CoQUOS system is characterized by two novel techniques, namely cluster-resilient random walk algorithm for propagating the queries to various regions of the network and dynamic probability-based query registration scheme to ensure that the registrations are well distributed in the overlay. Further, we also develop effective and efficient schemes for providing resilience to the churn of the P2P network and for ensuring a fair distribution of the notification load among the peers. This paper studies the properties of our algorithms through theoretical analysis. We also report series of experiments evaluating the effectiveness and the costs of the proposed schemes.