There is increasing evidence that cyclic and linear carbonates, commonly used solvents in Li ion battery electrolytes, are unstable in the presence of superoxide and thus are not suitable for use in rechargeable Li air batteries employing aprotic electrolytes. A detailed understanding of related decomposition mechanisms provides an important basis for the selection and design of stable electrolyte materials. In this article, we use density functional theory calculations with a Poisson-Boltzmann continuum solvent model to investigate the reactivity of several classes of aprotic solvents in nucleophilic substitution reactions with superoxide. We find that nucleophilic attack by O-2(center dot-) at the O-alkyl carbon is a common mechanism of decomposition of organic carbonates, sulfonates, aliphatic carboxylic esters, lactones, phosphinates, phosphonates, phosphates, and sulfones. In contrast, nucleophilic reactions of O-2(center dot-) with phenol esters of carboxylic acids and O-alkyl fluorinated aliphatic lactones proceed via attack at the carbonyl carbon. Chemical functionalities stable against nucleophilic substitution by superoxide include N-alkyl substituted amides, lactams, nitriles, and ethers. The results establish that solvent reactivity is strongly related to the basicity of the organic anion displaced in the reaction with superoxide. Theoretical calculations are complemented by cyclic voltammetry to study the electrochemical reversibility of the O-2/O-2(center dot-) couple containing tetrabutylammonium salt and GCMS measurements to monitor solvent stability in the presence of KO2 and a Li salt. These experimental methods provide efficient means for qualitatively screening solvent stability in Li air batteries. A clear correlation between the computational and experimental results is established. The combination of theoretical and experimental techniques provides a powerful means for identifying and designing stable solvents for rechargeable Li air batteries.