We propose a parallel algorithm for dynamic slicing of distributed Java programs. Given a distributed Java program, we first construct an intermediate representation in the form of a Distributed Program Dependence Graph (DPDG). We mark and unmark the edges of the DPDG appropriately as and when dependencies arise and cease during run-time. Our algorithm can run parallely on a network of computers, so that each node in the network contributes to the dynamic slice by computing its local portion of the global slice in a fully distributed fashion. Keywords program slicing, program dependence graph, distributed programming.