The rate constants of the H-abstraction reactions from CH3Cl and CH3Br molecules by ClO and BrO radicals have been estimated over the temperature range of 300-2500 K using four different levels of theory. Calculations of optimized geometrical parameters and vibrational frequencies are performed using B3LYP and MP2 methods combined with the cc-pVTZ basis set. Single-point energy calculations have been carried out with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (perturbatively) electron excitations CCSD(T) using the cc-pVTZ and cc-pVQZ basis sets. Canonical transition-state theory combined with an Eckart tunneling correction has been used to predict the rate constants as a function of temperature. In order to choose the appropriate levels of theory with chlorine- and bromine-containing species, the reference reaction Cl (P-2(3/2)) + CH3Cl -> HCl + CH2Cl (R-ref) was first theoretically studied because its kinetic parameters are well-established from numerous experiments, evaluation data, and theoretical studies. The kinetic parameters of the reaction R-ref have been determined accurately using the CCSD(T)/cc-pVQZ//MP2/cc-pVTZ level of theory. This level of theory has been used for the rate constant estimation of the reactions ClO + CH3Cl (R-1), ClO + CH3Br (R-2), BrO + CH3Cl (R-3), and BrO + CH3Br (R-4). Six-parameter Arrhenius expressions have been obtained by fitting to the computed rate constants of these four reactions (including cis and trans pathways) over the temperature range of 300-2500 K