The spontaneous solid state spreading of In, Ga and Cr oxides over the surface of Al2O3 and ZrO2(Y2O3) single crystals is reported. The film structure and element and phase composition was studied using a number of methods. The thermodynamic and kinetics aspects of oxide spreading and the subsequent crystallization on the surface of primary border films are discussed. The kinetic law of layer growth is determined and discussed. It is shown that mutual solubility as well as counter diffusion of the spread oxide and support components reduced the starting temperature and the activation energy of spreading.