The ability of uranium monoxide cations, UO+ and UO2+, to activate the O-H bond of H2O was studied by using two different approaches of the density functional theory. First, relativistic small-core pseudopotentials were used together with B3LYP hybrid functional. In addition, frozen-core PW91-PW91 calculations were performed within the ZORA approximation. A close description of the reaction mechanisms leading to two different reaction products is presented, including all the involved minima and transition states. Different possible spin states were considered as well as the effect of spin-orbit interactions on the transition state barrier heights. The nature of the chemical bonding of the key minima and transition states was studied by using topological methodologies (ELF, AIM). The obtained results are compared with experimental data, as well as with previous studies on the reaction of the bare uranium cations with water, to analyze the influence of the oxo-ligand in reactivity.