Earlier studies have shown that the most stable structures for (ZnS)n clusters with n = 10-47 are hollow polyhedral clusters ("bubbles"). We report a detailed study of larger clusters, where n = 50, 60, 70, and 80, for which onionlike or "double bubble" structures are predicted. We report calculations of the vibrational spectra and the electronic structure of bubble and double bubble clusters, which may assist in their experimental identification.