We investigate how universal the collective behavior, due to the many-body interactions in polydisperse hard-sphere systems, is at higher volume fractions. We perform two types of computer simulations, a Brownian-dynamics simulation on colloidal suspensions of hard spheres, where the hydrodynamic interactions between particles are neglected, and a molecular-dynamic simulation on atomic systems of hard spheres. Thus, we show that the long-time self-di usion coe cients D L S in both systems become singular as D L S ( ) ∼ (1 -= c) 2 because of the collective interactions due to the many-body collision processes, where is a particle volume fraction and c 0:586 for 6% polydispersity. Although D L S exhibits the same singular behavior as that obtained theoretically for the monodisperse suspension with the hydrodynamic interactions, no liquid-glass transition is found because even the polydisperse hard-sphere systems crystallize without the hydrodynamic interactions for all above the melting volume fraction, which is lower than c.