Electrochemical measurements are carried out on three-phase boundaries LaF₃:Eu²⁺/Me, oxygen gas, where Me = Ti, Be, Ta, Au and also on the boundaries of CeF₃:Sr²⁺ with Ag-supported Ag and Bi microelectrodes by the methods of linear scan voltammetry, chronoamperometry, and cyclic voltammetry. The conditions beneficial for reduction of oxygen gas, transformations of chemisorbed oxygen, and the appearance of its mobile forms are considered. Results on the interaction of gaseous oxygen with metals in contact with LaF₃:Eu²⁺ single crystals are generalized. The correlation is found between the oxygen reduction potential and the difference of electronegativities Δχ Me-O. The relationship is revealed between the oxygen reduction potential and the Me-Me bond energy by taking into account the structural factor f/k _n, where f is the number of binding electrons and k _n is the coordination number.