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Mobile ad hoc network and peer-to-peer networks are most advancing and emerging research areas in the recent years. Both of these networks are based on the same phenomenon like self-configuration and self-organization. Although, peer-to-peer network was firstly designed for wired network but now a days it may be deployed over mobile ad hoc network. When P2P networks are deployed over ad hoc network, it faces different problems due to dynamic topology and limited resources like memory, bandwidth and battery life of mobile nodes. In mobile ad hoc network nodes are continuously moving in a certain direction so network topology is changing from time to time. Node mobility is an important issue in these networks. Most of the researchers used only one mobility model in evaluation of routing protocols in mobile peer-to-peer network. As mobility models plays an important role in evaluation of the performance of different protocols, so other mobility models should also be used. We consider two mobility models probabilistic random walk and freeway mobility model in this network and we also compare these results with already used random waypoint mobility model. We used an ad hoc routing protocol Ad hoc On Demand Distance Vector routing under a peer-to-peer network application to evaluate the performance under prescribed mobility model. The results have been validated using network simulator (NS-2) and this helped in choosing proper mobility model for specific environment.