Charging of services in a distributed system will become more and more important for systems which are utilized commercially. Such an important distributed system exists in form of a Computational Grid (CG), offering a variety of services on different layers to many users, academic and industrial ones. Although by itself a CG defines a research and operational problem area, the dedicated task of charging CG services, by definition a new grid service, has to be considered crucial, once a large number of users will share computational resources as well as services offered by a CG. The potential synergies for applying a similar concept to all layers and different types of services within a Computational Grid should be exploited. Safely assuming that the Internet will form the all-embracing communication technology in use in the near future, Differentiated Services Architecture-based communication layer services will offer the potential to differentiate higher layer and distributed services of the CG.