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Peer-to-peer (P2P) networking is used by users with similar interests to exchange, contribute, or obtain files. This network model has been proven popular to exchange music, pictures, or software applications that are saved, and most likely executed at the downloading host. At the expense of this mechanism, worms, viruses, and intruding files find an open front door to the downloading host and giving them place to a very convenient environment for successful proliferation throughout the network. Although virus detection software are currently available, this countermeasure works in a reactive approach and most times isolated manner. In this paper, we consider a trust management scheme to contain the proliferation of viruses in P2P networks. Specifically, we propose a trust management system based on a two-layer approach to bound the proliferation of viruses. The new scheme is called Double-layer Dynamic Trust (DDT) management scheme. Our results show the proposed scheme bounds virus proliferation. With this approach, the number of infected hosts and proliferation rate are limited to small values. We compare our results to other existing approaches.