Taking into account the intrinsic heterogeneity of communication latency of grid environments, we propose in this article a composition approach that enables to build mutual exclusion services for grids. By using our approach, different intra and inter cluster token-based mutual exclusion algorithms can be combined easily. Performance evaluation tests were conducted on the French national grid testbed called Grid'5000, whose results show that our approach is effective and that the choice of the most suitable inter cluster algorithm depends on the behavior of the application.