In a previous paper~\cite{HPCS2002}, 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 such algorithms. After proposing a non-centralized version of dynamic load balancing which is best suited to asynchronism, we verify its efficiency by some experiments on a general Partial Differential Equation (PDE) problem. Finally, we give some general conditions for the use of load balancing to obtain good results with this kind of algorithms and discuss the choice of the residual as an efficient load estimator.