Abstract Efficient communication is the basis of an implementation of a parallel language on a distributed machine architecture. This article handles about the communication mechanism that is needed to support parallel graph rewriting in Concurrent Clean. The danger of deadlock is imminent at several levels of such a system. Communication problems and their solutions are closely related to memory management issues, garbage collection in particular. In fact the communication mechanism presented here is a global memory management system. It is part of a distributed runtime system that has been moulded to fit parallel graph rewriting as implemented in Concurrent Clean.