Magnetism of capped nanoparticles, NPs, of non-magnetic substances as Au and ZnO is briefly reviewed. The source of the magnetization is discussed on the light of recent X-ray magnetic circular dichroism experiments. As magnetic dichroism analysis has pointed out impurity atoms bonded to the surface act as donor or acceptor of electrons that occupy the surface states. It is proposed that mesoscopic collective orbital magnetic moments induced at the surface states can account for the experimental magnetism characteristic of these nanoparticles. The total magnetic moment of the surface originated at the unfilled Fermi level can reach values as large as 102 or 103 Bohr magnetons.