The dynamical properties for the two hydrogen-abstraction reactions of 1,1,1-trichloroethane (CH3CCl3) and 1,1,1-trifluoroethane (CH3CF3) with chlorine atoms over the temperature range 200-1200 K are investigated theoretically. The minimum energy paths (MEPs) of both reactions are calculated at the BH&H-LYP/6-311+G(d,p) level, and the energies along the MEPs are further refined at the CCSD(T)/6-311+G(2df, 2p)(single-point) level. For both reactions, the theoretical rate constants are in good agreement with available experimental results. Compared with the one previous theoretical investigation at the HF/6-31G(d) level followed by BAC-MP4 single-point energy calculations, our calculated rate constants are closer to the experimental values. The theoretical results show that for the title reactions the variational effect is small over the whole considered temperature range and the small-curvature tunneling effect is only important in the lower temperature range.