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Grid computing and peer-to-peer computing are both hot topics at present. The convergence of the two systems is increasingly visible, and OGSA provides a framework for integrating grid and peer to peer. However, grid resource discovery is a key issue for peer-to-peer grid. In contrast with the traditional grid resource discovery algorithm, genetic ant algorithm firstly uses genetic algorithm to find the coarsest GridPeer resources quickly, then to find accurate resources through the ant algorithm. Theoretical analysis and simulations prove that genetic ant algorithm in peer-to-peer grid can improve the performance of resource discovery.