The kinetics of the reactions of BrO radicals with HO2 and DO2 radicals, HO2 + BrO --> products (1) and DO2 + BrO --> products (3), have been studied by the mass spectrometric discharge flow method at temperatures between 230 and 360 K and at a total pressure of 1 Torr of helium. The rate constant of reaction 1 as determined by monitoring either the HO2 or the BrO decay tin excess of BrO or HO2, respectively) is given by the Arrhenius expression k(1) = (9.4 +/- 2.3) x 10(-12) exp[(345 +/- 60)/T] cm(3) molecule(-1) s(-1), with k(1) = (3.1 +/- 0.8) x 10(-11) cm(3) molecule(-1) s(-1) at T = 298 K, where the uncertainties represent 95% confidence limits and include estimated systematic errors. The rate constant of reaction 3, measured under pseudo-first-order conditions in an excess of BrO, is k(3) = (3.9 +/- 1.2) x 10(-12) exp[(410 +/- 80)/T] cm(3) molecule(-1) s(-1), with k(3) = (1.6 +/- 0.4) x 10(-11) cm(3) molecule(-1) s(-1) at T = 298 K, where the uncertainties represent 95% confidence limits and include estimated systematic errors. The value of k(3) was measured for the first time, whereas the value of k(1) was compared with those from previous studies. From the observation that no ozone formed among the products of thr: HO2 + BrO reaction, an upper limit was derived for the channel HO2 + BrO --> HBr + O-3 (1b) of reaction 1: k(1b)/k(1) < 0.004 at T = 298 K. The implication of this result for stratospheric bromine partitioning is briefly discussed.