The rate constants for the gas-phase reactions of hydroxyl radicals and ozone with the biogenic hydrocarbons beta-ocimene, beta-myrcene, and alpha- and beta-farnesene were measured using the relative rate technique over the temperature ranges 313-423 (for OH) and 298-318 K (for O-3) at about 1 atm total pressure. The OH radicals were generated by photolysis of H2O2, and O-3 was produced from the electrolysis of O-2. Helium was used as the diluent gas. The reactants were detected by online mass spectrometry, which resulted in high time resolution, allowing large amounts of data to be collected and used in the determination of the Arrhenius parameters. The following Arrhenius expressions have been determined for these reactions (in units of cm(3) molecules(-1) s(-1)): for beta-ocimene + OH, k = (4.35(-0.66)(+0.78)) x 10(-11) exp[-(579 +/- 59)/T]; for beta-ocimene + O-3, k = (3.15(-0.95)(+1.36)) x 10(-15) exp[-(626 +/- 110)/T]; for beta-myrcene + O-3, k = (2.21(-0.66)(+0.94)) x 10(-15) exp[-(520 +/- 109)/T]; for a-farnesene + OH, k(OH) = (2.19 +/- 0.11) x 10(-10) for 323-413 K; for alpha-farnesene + O-3, k = (3.52(-2.54)(+9.09)) x 10(-12) exp[-(2589 +/- 393)/T]; for beta-farnesene + OH, k(OH) = (2.88 +/- 0.15) x 10(-10) for 323-423 K; for beta-farnesene + O-3, k = (1.811) x 10(-12) exp[-(2347 +/- 329)/T]. The Arrhenius parameters here are the first to be reported. The reactions of alpha- and beta-farnesene with OH showed no significant temperature dependence. Atmospheric residence times due to reactions with OH and O-3 were also presented.