Reactions of alkyl radicals with oxygen are key reactions in the low-temperature oxidation of hydrocarbons, but they have not been extensively studied yet in the case of cycloalkanes. Isomerizations of cycloalkylperoxy radicals and formation of cyclic ethers are especially important. In the present work, a theoretical study of the gas-phase reactions of cyclopentylperoxy and cyclohexylperoxy radicals has been carried out by means of quantum chemical calculations at the CBS-QB3 level. Computations on cyclopentylperoxy decomposition pathways are reported here for the first time. Thermochemical data have been obtained by means of isodesmic reactions, and the contribution of hindered rotors has been explicitly taken into account. Transition state theory has been used to calculate rate constants for all the elementary reactions. Three-parameter Arrhenius expressions have been derived in the temperature range 300-1000 K. Tunneling effects have been accounted for in the case of H-atom transfers. Our results compare well with experimental data and previous calculations available in the literature. In particular, the predicted rate constants for processes involving cyclohexylperoxy radicals, which have been introduced in a reaction mechanism scheme proposed before, exhibit excellent agreement with experiments at low and intermediate temperatures.