The oxidation processes in the industrial production of aluminum from cryolite melts are not fully understood. Oxidation of AlOF2- leads initially to AlOF2 radicals. The structure of the AlOF2 dimer and several oxidized and reduced forms of this compound are investigated by theoretical methods and compared to analogous boron and gallium compounds, The thermodynamic stability of these compounds is investigated. It is shown that the dimeric compound of AlOF2 contains a symmetric peroxo bridge and is unexpectedly stable toward decomposition.