In this paper we discuss a hierarchical relaxation method for solving a system of equations. The method proceeds by adjoining to a given system of equations whose solution is sought, an auxiliary hierarchy of systems. The relaxation procedure consists of a judicious mixing of relaxation steps in the different members of the hierarchy. When the choice of the hierarchy and the mixing of relaxation steps are appropriate, the entire procedure provides an acceleration of the relaxation process toward a determination of the solution of the original system. The procedure lends itself to parallel implementation, even in an asynchronous mode. We discuss these aspects of hierarchical relaxation as well. © 1979 Springer-Verlag.