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A peer to peer (P2P) computer network relies on direct connections between participants rather than conventional centralized resources. These networks are useful for many purposes, but the ldquokiller-apprdquo nowadays is file sharing. BitTorrent is a very popular protocol for this matter. In this paper we model a BitTorrent network as a multi-agent system. In it, each BitTorrent client is an agent that interacts with other agents and reacts autonomously, following some algorithms. Its objectives are downloading a content in the shortest time possible, and sharing it with other agents. The model is programmed in JADE, a software framework in Java language for agent development. The model has been validated by initial tests, and it was used to study the behavior of BitTorrent networks in diverse situations hard to test in a real network.