Absolute rate constants have been measured for the reactions of cumylperoxy radicals with a number of hydrocarbons. The cumylperoxy radicals were produced from cumene hydroperoxide. Sufficient hydroperoxide was present to ensure that only cumylperoxy radicals were involved in the rate-determining propagation reaction.Primary and secondary deuterium isotope effects have been measured for propagation and termination in the oxidation of cumene. The rate of hydrogen atom abstraction from ring-substituted cumenes by cumylperoxy radicals can be correlated by the Hammett equation using o* substituent constants, p = -0.29. Primary and secondary peroxy radicals are about 3-5 times more reactive in hydrogen abstraction than tertiary peroxy radicals.