We propose a new composition approach to mutual exclusion algorithms for applications spread over a grid which is composed of a federation of clusters. Taking into account the heterogeneity of communication latency, our hierarchical architecture combines intra and inter cluster algorithms. We focus on token-based algorithms and study different compositions of algorithms. Performance evaluation tests have been conducted on a national grid testbed whose results show that our approach is scalable and that the choice of the most suitable inter cluster algorithm depends on the behavior of the application.