The hydoxylation degree of ZrO2 and HfO2 interfaces is a key factor for both the film growth rate of the corresponding oxides in the ALD process and for the catalytic activity of the deposited films. Therefore, the aim of this work was to determine the energies adsorption on various ZrO2 and HfO2 surfaces as functions of the surfaces coverage. In accordance with experimental data on ZrO2 and HfO2 ALD processes, we considered the (001) and (101) surfaces of t-ZrO2 and the (001) surface of monoclinic hafnia and zirconia. First principle calculations were carried out with the use of the plane wave DFT and by ab-initio cluster calculations. All periodic structure calculations were done with GGA correction term, whereas hybrid functionals were used for cluster models. In our calculations water adsorption energy strongly depends on surface hydroxylation degree: adsorption energy for (001) t-ZrO2 decreases from 120 kJ/mol to 40 kJ/mol when the surface coverage reaches 100%. Similar results were obtained for the other surfaces considered here. It was speculated that this dependence can be partially explained by dipole-dipole interactions at the surface. We note reasonable agreement between adsorption energies calculated in periodic type calculations and cluster models. The dependence of the adsorption energy obtained in our study can explain experimental temperature dependence of the film growth rate.