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In a file system, critical sections are represented by means of read or write operations on useful data (i.e files) as well as metadata of the system. The processes must be synchronized to reach these shared resources, thanks to mutual exclusion algorithms which guarantee data consistency. In a grid environment, processes are compared to grid nodes and their synchronization is ensured by the sending of messages on the network. Moreover, the access time to a critical section is conditioned by the high latency of the network. In this paper, we propose a method based on the use of the multicast, which makes it possible in some cases to decrease the access time to critical sections. This solution was implemented within a token- and tree-based distributed mutual exclusion algorithm and it was integrated in the grid middleware named ViSaGe.