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Peer-to-peer (P2P) computing grids consist of peer nodes that communicate directly among themselves through wide-area networks and can act as both clients and servers. These systems have drawn much research attention since they promote Internet-scale resource and service sharing without any administration cost or centralized infrastructure support. However aggregating different application services into a high-performance distributed application delivery in such systems is challenging due to the presence of dynamic performance information, arbitrary peer arrivals/departures, and systems' scalability requirement. In this paper we propose a scalable QoS-aware service aggregation model to address the challenges. The model includes two tiers: (1) on-demand service composition tier which is responsible for choosing and composing different application services into a service path satisfying the user's quality requirements; and (2) dynamic peer selection tier, which decides the specific peers where the chosen services are actually instantiated based on the dynamic, composite and distributed performance information. The model is designed and implemented in a fully distributed and self-organizing fashion. Conducting extensive simulations of a large-scale P2P system (104 peers), we show that our proposed model and algorithms achieve better performance than several common heuristic algorithms.