Abstract. We study in this paper several scheduling heuristics for GridRPC middlewares. When dealing with performance issue, the scheduling strategy is one of the most important feature. However, many heuristics implemented in available middlewares were not designed for this context (for instance MCT in NetSolve). Therefore, schedulers are not necessarily effective. We propose to use heuristics based on a non-intrusive module which is able to estimate the duration of all tasks in the system. Three criteria are examined among which the execution time of the application, e.g. the makespan. Experiments on a real platform show that the proposed heuristics outperform MCT for at least two of these three criteria. Keywords : time-shared and heterogeneous resources, dynamic scheduling heuristics, historical trace manager, completion dates estimations, DAGs