Density functional molecular cluster calculations have been used to investigate the interaction of SO2 with defect-free TiO2(110) and Ti2O3(1012) surfaces. Adsorbate geometries and chemisorption enthalpies have been computed and discussed. Several local minima have been found for TiO2(110), but only one seems to be relevant for the catalytic conversion of SO2 to S. In agreement with experiment, the bonding of SO2 to Ti2O3(1012) is much stronger than that on TiO2(110). Moreover, our results are consistent with the surface oxidation and the formation of strong Ti-O and Ti-S bonds. On both substrates, the bonding is characterized by a two-way electron flow involving a donation from the SO2 HOMO into virtual orbitals of surface Lewis acid sites (L-s(a)), assisted by a back-donation from surface states into the SO2 LUMO. However, the localization of surface states and the strength of back-donation are very different on the two surfaces. On TiO2(110), back-donation is weaker, and it involves unsaturated bridging O atoms, while on Ti2O3(1012), it implies the Q-based valence band maximum and significantly weakens the S-O bond.