The metal air battery use free oxygen from the air to react with metal ions on the surface of the air (oxygen) electrode, which is much lighter than conventional cathodes used in Li-ion batteries. However, the fundamental challenge that limits the use of metal air battery technology is the ability to find a catalyst that will catalyse the formation and decomposition of discharge products during charging and discharging cycle i.e. oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). Density functional theory (DFT) study is employed in order to investigate the surfaces of, (Rutile) R-MnO₂, TiO₂ and VO₂ (MO₂) which act as catalysts in metal-air batteries. Adsorption and co-adsorption of metal (K/Mg) and oxygen on (110) β-MO₂ surface is investigated, which is important in the discharging and charging of K/Mg–air batteries. Due of the size of the supercell, and assuming that oxygen atoms occupy bulk-like positions around the surface metal atoms, only five values of (gamma) Γ are possible if constraint to a maximum of 1 monolayer (ML) of adatoms or vacancies: Γ= 0 surface is the stoichiometric surface, Γ= 1, 2 are the partially and totally oxidised surfaces, and Γ=-1, -2 are the partially and totally reduced surfaces. The manganyl, titanyl and vanadyl terminated surface are not the only surfaces that can be formed with Γ= +2, oxygen can be adsorbed also as peroxo species (O₂)^2-, with less electron transfer from the surface vanadium atoms to the adatoms than in the case of manganyl, titanyl or vanadyl formation. The Mg orientation between two bridging oxygen and in-plane oxygen (bbi) orientation is much more stable for the three metal oxides, thus Mg generally prefers to adsorb where it will be triply coordinated to two bridging oxygens and one in-plane oxygen atom. However, K prefers to position itself between the two in-plane oxygens and a bridging oxygen on the surface.