This paper describes a methodology for the implementation of asynchronous parallel iterative algorithms, which is the domain decomposition method. This approach reduces the cost of synchronization that affects synchronous algorithms. As an application of the proposed approach, the algorithms based on the well-known point-SOR methods are presented in both synchronous and asynchronous forms. Results obtained using the MIMD (Multiple Instruction stream Multiple data stream) superparallel computer are given, for the model problem of the solution of a Poisson equation.