Grids are distributed systems aiming at the aggregation of geographically distributed resources for high performance computing. Heterogeneity and volatility are the main characteristics of resources in a Grid environment. This aspect makes the resource discovery in a grid a crucial problem: Given the resource requirements of an application, a resource discovery mechanism returns the set of resources matched by the description. By considering a grid as a peer-to-peer network, it is possible to use decentralized algorithms to locate resources. We propose in this paper a new mechanism for peer-to-peer resource discovery in a grid environment. Our system is based on push-pull strategy,i.e, each peer may ask for resources or advertise them if they are available. Also, each peer maintains a local cache of messages and uses this information for routing. We compare our proposal with other search methods through simulation and we show that it provides??higher success rate with lower overhead.