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The massive amount of resources on computational grids raises the question of efficient resource discovery and selection. In this paper we present an agent-based approach to these two phases of a grid scheduling process. The approach is based on client agents which act on behalf of grid users, and search for resources in a network of resource representatives that are registries of resource characteristics. After potentially suitable resources are discovered, client agents carry out negotiations directly with agents representing local resource management systems. This selection process first determines the willing resources with a contract-net protocol and then uses current load information and a more accurate post-discovery search to determine the optimum set of resources for the task in hand