Alkali metal-air batteries are important candidates for next generation power sources due to their high energy density. One academic challenge before wide application of the Li/Na-O-2 batteries lies in the understanding of the formation and dissociation of the discharge products like Li/Na oxides, peroxides and superoxides. This is associated with the bonding interactions in these solid state compounds. In this paper, the ionic bonds between the positively charged Li+/Na+ ions and the negatively charged O-2 groups, as well as the O-O covalent bonds within the O-2 groups (O-2(-) and O-2(2-)) are studied from first principles calculations. The results shed lights to the charge/discharge potential and the formation and decomposition of the discharge products. It is found that ionic bonds in the discharge products play more important role in determining the discharge potential in the peroxides and superoxides, while the decomposition of these discharge products and thus cycling of the battery has strong relevance with the weakened O-O covalent bonds in the negatively charged O-2 groups. (C) 2017 Elsevier B.V. All rights reserved.