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Reactive halogen species (ClO and BrO) play a critical role in the stratospheric ozone depletion. However, the reactivity of these radical moieties with volatile organic compounds is also important in determining the composition of the Earth's atmosphere. In this study, the reactions of BrO and ClO radicals with a series of smaller linear alkanes (CnH2n+2, n = 1,2,3, and 4) were studied using the CCSD(T)/CBS//B3LYP/cc-pVTZ level of theory. The kinetics of the title reactions were evaluated using the Canonical Variational Transition (CVT)/Small Curvature Tunneling (SCT)/Interpolated Single Point Energy (ISPE) methodology over the studied temperature range of 200-3000 K. H-abstraction from the nonterminal carbon was found to be thermodynamically and kinetically favorable in comparison to abstraction of H atom from the primary carbon. On a per-hydrogen basis at 298 K, BrO and ClO are focused to abstract the secondary hydrogens of C3H8 faster than the primary hydrogens by factors of 40 and 110, respectively. On the other hand, for n-C4H10 at the same temperature, the per-hydrogen preferences for secondary H atoms are found to be factors of 220 and 270 for BrO and ClO, respectively. To aid in modeling the stratospheric environment and combustion regime, three parameter fits to the computed rate constants between 200 and 3000 K are provided. The branching ratios and thermochemical parameters for the various reaction channels are also discussed in this paper.