Recently, a method of fabricating hollow nanospheres of cobalt selenide and cobalt sulphide has been announced (Y. Yin et al. Science Vol. 304, p711 (2004). We have investigated the stability and mechanism of collapse of hollow nanospheres by the method of Molecular Dynamics. First of all, we have analyzed single metallic systems exemplified by Pd. We found that for small hollow nanospheres up to about 10 000 atoms, the spheres collapsed quickly but not by vacancy-assisted mechanisms but by a mechanism involving Shockley partial dislocations. For larger hollow nanospheres, too much energy is required for that mechanism and the most likely mechanism for sphere collapse, now far slower, involves the vacancy mechanism.