The enhancement of the catalytic efficiency of semiconducting oxides by surface defects has led to intense experimental activity on their electronic and structural properties. By making use of the scattering theoretical method, we have investigated the electronic properties of point defects on the (110) face of two oxides of rutile structure: SnO2 and TiO2. A comparative study of various defect configurations is presented. For SnO2, which has a simple metal cation, we find no surface defect state inside the gap. The surface defect density of states presents essentially O-p derived resonances in the valence-band region and Sn-s derived resonances in the conduction-band region. For the transition metal oxide TiO2, we obtain similar features when O atoms are removed in the surface layer. However, in the case of a subsurface vacancy, we find a Ti-d derived surface defect state inside the gap. When allowance is made for relaxation of the atoms around the vacancy, this state is located at 0.7 eV below the conduction-band edge, in agreement with experimental results. The physical mechanism at the origin of this surface defect state is elucidated.