The results of studying the surface spreading of In, Ga, and Cr oxides over the Al2O3 and ZrO2(Y2O3) single crystals are presented. It has been established that the spontaneous solid state spreading of oxide-diffusers over the single crystal surface conjugated with the formation of solid solutions occurs in the systems In2O3-ZrO2(Y2O3), Ga2O3-Al2O3, and Cr2O3-Al2O3. No spreading of the diffuser over the substrate is observed in the systems Ga2O3-ZrO2(Y2O3) and Cr2O3-ZrO2(Y2O3). The structure, element and phase compositions of the films formed have been studied by a complex of methods. The dependences of the efficiency of diffuser spreading on the type of the phase diagram of the system, and the compatibility of the crystal structures and parameters of the crystalline lattice of the diffuser and substrate have been discussed. The kinetics of film growth has been studied and examined. The temperature (700-1550°C) effect on the solid state spreading during annealing in air has been studied. The effective activation energies of solid phase spreading have been determined. It has been shown that the formation of solid solutions and the mutual diffusion of the components of the diffuser and substrate favor a decrease in the temperature of the beginning of solid state spreading and a decrease in the effective activation energy of the process.