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In a previous work, we have shown the very high power of asynchronism for parallel iterative algorithms in a global context of grid computing. In this article, we study the interest of coupling load balancing with asynchronism in these algorithms. We propose a non-centralized version of dynamic load balancing which is best suited to asynchronism. After showing, by some experiments on a given ODE problem, that this technique can efficiently enhance the performance of our algorithms, we give some general conditions for the use of load balancing to obtain good results with this kind of algorithm.