Quantum chemical analysis of coordination of nitroxides on the surfaces of alumina, gallia, and silica is performed. Structural, magnetic resonance and energy characteristics of coordination are calculated. Different cluster models of the surface acid sites (AS) are tested. The results of ESR experiments are interpreted. The comparison of Lewis acid sites (LAS) of alumina and gallia surfaces is carried out. Different ways of coordination of nitroxides with two electron-donating groups are analyzed.