Finding suitable solvents remains one of the most elusive challenges in rechargeable, nonaqueous Li-air battery technology. Although ether and amides are identified as stable classes of aprotic solvents against nucleophilic attack by superoxide, many of them are prone to autoxidation under oxygen atmosphere. In this work, we use density functional theory calculations coupled with an implicit solvent model to investigate the autoxidative stability of ether- and N,N-dialkylamide-based solvents. The change in the activation free energy for the C-H bond cleavage by O-2 is consistent with the extent of peroxide production for each class of solvent. Conversely, the thermodynamic stability alone is not sufficient to account for the observed variation in solvent reactivity toward O-2. A detailed understanding of the factors influencing the autoxidative stability provides several strategies for designing molecules with enhanced air/O-2 stability, comparable or superior to that of structurally related hydrocarbons. The mechanism of superoxide-mediated oxidation of hydroperoxides derived from ethers and amides is presented. The degradation mechanism accounts for the primary decomposition products (esters and carboxylates) observed in the Li-air battery with ether-based electrolytes. The identification of solvents having resistance to autoxidation is critical for the development of rechargeable Li-air batteries with long cycle life.