The Explicitly Restarted Arnoldi Method (ERAM) allows to find a few eigenpairs of a large sparse matrix. The Multiple Explicitly Restarted Arnoldi Method (MERAM) is a technique based upon a multiple projection of ERAM and accelerates its convergence [3]. The MERAM allows to update the restarting vector of an ERAM by taking the interesting eigen-information obtained by the other ones into account. This method is particularly well suited to the GRID-type environments. We present an adaptation of the asynchronous MERAM for NetSolve global computing system. We point out some advantages and limitations of this kind of systems to implement the asynchronous hybrid algorithms. We give some results of our experiments and show that we can obtain a good acceleration of the convergence compared to ERAM. These results show also the interest of the MERAM-like hybrid methods for the GRID computing environments.