Grids as infrastructures offer access to computing, storage and other resources in a transparent way. The user does not have to be aware where and how the job is being executed. Grid clusters in particular are an interesting target for running computation-intensive calculations. Running MPI-parallel applications on such clusters is a logical approach that is of interest to both computer scientists and to engineers. This paper gives an overview of the issues connected to running MPI applications on a heterogenous Grid consisting of different clusters located at different sites within the Int.EU.Grid project. The role of a workload management system (WMS) for such a scenario, as well as important modifications that need to be made to a WMS oriented towards sequential batch jobs for better support of MPI applications and tools are discussed. In order to facilitate the adoption of MPI-parallel applications on heterogeneous Grids, the application developer should be made aware of performance problems, as well as MPI-standard issues within its code. Therefore tools for these issues are also supported within Int.EU.Grid. Also, the special case of running MPI applications on different clusters simultaneously as a more Grid-oriented computational approach is described.