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In this paper we develop a model for random walk search mechanism in unstructured P2P networks. Using the model we obtain analytical expressions for the performance metrics of random walk search in terms of the popularity of the resource being searched for and the parameters of random walk. We propose an equation based adaptive search mechanism that uses estimate of popularity of a resource in order to choose the parameters of random walk such that a targeted performance level is achieved by the search. We also propose a low-overhead method for maintaining an estimate of popularity that utilizes feedback (or lack there-off) obtained from previous searches. Simulation results show that the performance of the equation based adaptive search is significantly better than the non-adaptive random walk.