Resource management in the typical Grid environment based on multi-MPP systems or clusters today still is one of the challenging problems. We will present MeSch, a solution for the problem of resource allocation and job scheduling in a distributed heterogeneous environment. MeSch has been implemented and tested successfully in the heterogeneous multi-MPP environment of GMD's Institute for Scientific Computing and Algorithms. MeSch allows users to access simultaneously, through a single request, heterogeneous resources distributed across the linked systems. This is possible either through explicit demands for different resources or through implicit scheduling of resources resulting from interpretation of requests. The scheduling system is available for both batch and interactive usage of resources. MeSch is implemented based on locally available scheduling facilities thus respecting the different scheduling systems and policies of the computing centers in the Grid.