The hydrogen-abstraction reactions of the radical NH(X(3)Sigma(-)) with methane and ethane have been studied by using ab initio molecular orbital theory and the canonical variational transition-state theory. The geometries of the reactants, transition states, and products were optimized at the UHF, UMP2, UMP4(sdq), and UQCISD levels of theory, and the forward and reverse reaction potential barriers were calculated accurately at the UQCISD(T)/6-311+G(3df,2p) and Gaussian 2 levels. The reaction paths were calculated by the intrinsic reaction coordinate theory at the UMP2/6-311G** level. The changes of the geometries and generalized normal-mode vibrational frequencies along the IRC were discussed. The energy profile along the IRC was further improved by the Gaussian 2 method. The forward and reverse reaction rate constants for the temperature range from 300 to 2000 K were evaluated by the conventional transition-state theory and the canonical variational transition-state theory with a small curvature tunneling correction. The theoretical rate constants of the forward and reverse reactions are all in good agreement with the experimental ones in the measured temperature range.