The results of density functional theory potential surface investigations are presented for small ZnS, ZnSe, CdS, and CdSe clusters, up to the heptamer. Clusters of CdSe are investigated further by geometry optimizations of larger crystal structure sections with up to 198 atoms that correspond to the wurtzite modification. In addition to structures and energies of these clusters, we present electron affinities, ionization potentials as well as electronic excitation spectra, obtained from time dependent density functional theory.