Using relative rate techniques, rate constants for the gas phase reactions of OH radicals and NO3 radicals with the sesquiterpenes alpha-cedrene, alpha-copaene, beta-caryophyllene, alpha-humulene, and longifolene have been measured at 296 +/- 2 K and atmospheric pressure of air. The rate constants obtained (in units of 10(-11) cm(3) molecule(-1) s(-1)) for the OH radical and NO3 radical reactions, respectively, are alpha-cedrene, 6.7 +/- 1.4 and 0.82 +/- 0.30; alpha-copaene, 9.0 +/- 1.9 and 1.6 +/- 0.6; beta-caryophyllene, 20(-9)(+5) and 1.9 +/- 0.8; alpha-humulene, 29(-10)(+7) and 3.5 +/- 1.3; and longifolene 4.7 +/- 1.0 and 0.068 +/- 0.021, where the indicated errors include the estimated overall uncertainties in the rate constants for the reference compounds. These rate constants and those for the corresponding O-3 reactions are combined with estimated ambient lower tropospheric concentrations of OH radicals, NO3 radicals, and O-3 to allow the lifetimes of these sesquiterpenes with respect to these chemical loss processes to be calculated. The sesquiterpenes studied are all reactive, with calculated overall lifetimes of a few hours or less. In particular, beta-caryophyllene and alpha-humulene are highly reactive toward O-3 and NO3 radicals, with calculated lifetimes due to these reactions of 1-2 min, and beta-caryophyllene and alpha-humulene are therefore not expected to be present in ambient air at measurable concentrations.