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Optimizing a given software system to exploit the features of the underlying system has been an area of research for many years. Recently, a number of self-adapting software systems have been designed and developed for various computing environments. In this paper, we discuss the design and implementation of a software system that dynamically adjusts the parallelism of applications executing on computational Grids in accordance with the changing load characteristics of the underlying resources. The migration framework implemented by our software system is aimed at performance-oriented Grid systems and implements tightly coupled policies for both suspension and migration of executing applications. The suspension and migration policies consider both the load changes on systems as well as the remaining execution times of the applications thereby taking into account both system load and application characteristics. The main goal of our migration framework is to improve the response times for individual applications. We also present some results that demonstrate the usefulness of our migration framework. Published in 2005 by John Wiley & Sons, Ltd.This article is a U.S. Government work and is in the public domain in the U.S.A.