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Alkylperoxyl (RO 2) and hydroperoxyalkyl (QOOH) species are crucial intermediates produced during the autoignition of transport fuels, and consequently their thermodynamic and kinetic data are very important. Since these data are not available experimentally, we take up the challenge of computing them from first principles. We compare the 1,5 shifts in 2-methyl-4-heptylperoxyl radical and 3-methylcyclohexylperoxy radical to clarify the similarities and differences of the kinetics of chain alkanes and cycloalkanes in the fuel oxidation mechanism. In order to take account of the multistructural and coupled torsional anharmonicity, we employ multistructural canonical variational transition state theory (MS-VTST) with multidimensional tunneling to calculate rate constants. The calculations explicitly include all conformers: 6 and 154 for the two reactants, 7, 6, 1, and 1 for the four transition states, and 289, 282, 8, and 5 for the four products (which are the reactants for the reverse reactions). The effects of various factors on the thermodynamic data and calculated rate constants are evaluated in detail. We found that multistructural torsional anharmonicity has a very large effect on the rate constants. This work illustrates how modern density functional and dynamics methods make it possible to calculate accurate rate constants for both branched-chain and cycloalkane peroxy radicals and hydroperoxy species. [ABSTRACT FROM AUTHOR]