The scope of this work is to study at atomistic level the mechanism of hydrogen spillover promoted by metal particles on oxide surfaces. By means of Density Functional Theory calculations with Hubbard correction (DFT+U) we have analyzed the adsorption and dissociation of molecular hydrogen on anatase titania, a-TiO 2 (101), and tetragonal zirconia, t-ZrO 2 (101), surfaces in the presence of a supported Ru 10 nanocluster. The role of the supported metal particle is essential as it favours the spontaneous dissociation of H 2 , a process which does not occur on the bare oxide surface. At low hydrogen coverage, the H atoms prefer to stay on the Ru 10 particle, charge accumulates on the metal cluster, and reduction of the oxide does not take place. On a hydroxylated surface, the presence of a Ru nanoparticle is expected to promote the reverse effect, i.e. hydrogen reverse spillover from the oxide to the supported metal. It is only at high hydrogen coverage, resulting in the adsorption of several H 2 molecules on the metal cluster, that it becomes thermodynamically favourable to have hydrogen transfer from the metal to the O sites of the oxide surface. In both TiO 2 and ZrO 2 surfaces the migration of an H atom from the Ru cluster to the surface is accompanied by an electron transfer to the empty states of the support with reduction of the oxide surface.