Crystalline cadmium sulfide is a semiconductor for which the wurtzite and zinc blende structures are energetically almost degenerate. Due to quantum-confinement effects, it is possible to tune the optical properties of finite cadmium sulfide clusters by varying their size. Here, we report results of a theoretical study devoted to the properties of stoichiometric CdnSn, clusters as a function of their size n. We have optimized the structure, whereby our initial structures are spherical pans of either of the two crystal structures, and we have studied systems with up to almost 200 atoms. The calculations were performed by using a simplified LCAO-DFT-LDA scheme. The results include the structure, electronic energy levels (in particular the frontier orbitals HOMO and LUMO), and stability as a function of size. The results allow for a unique definition of a surface region. The Mulliken populations indicate that the bonds within this region are more ionic than in the bulk. Furthermore, whereas the HOMO is delocalized over major parts of the nanoparticle, the LUMO is a surface state, which confirms recent experimental findings. Finally, the relative stability of the zinc blende and wurtzite structures is strongly dependent on the size of the system, and there is a close connection between the HOMO-LUMO energy gap and stability.