We study the stability of rotating collisionless self-gravitating spherical systems by using highresolution N-body experiments on a Connection Machine CM-5.We added rotation to Ossipkov±Merritt (OM) anisotropic spherical systems by using twomethods. The first method conserves the anisotropy of the distribution function defined in the OM algorithm. The second method distorts the systems in velocity-space. We then show that the stability of systems depends both on their anisotropy and on the value of the ratio of the total kinetic energy to the rotational kinetic energy. We also test the relevance of the stability parameters introduced by Perez et al. for the case of rotating systems