In the present work, we have theoretically calculated the rate constants and their temperature dependence for the reactions CHnD4-n+OH -->P, and for the reaction of methane with OD, by means of variational transition-state theory plus multidimensional tunneling corrections, at the MP-SAC2//MP2/cc-pVTZ/// and CCSD(T)//MP2/cc-pVTZ/// electronic levels. Also, the newly developed single-point energy interpolation algorithm has been used at the CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ and CCSD(T)-SAC//MP2/cc-pVTZ levels. For reactions with n=1, 2 or 3, the competitive canonical unified statistical theory has been applied as they involve more than one nonequivalent reaction channel. Variational effects and tunneling have been found to be very important. The proton shift classical energy barrier turns out to be 5.83 and 4.97 kcal/mol at the CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ and CCSD(T)-SAC//MP2/cc-pVTZ levels, respectively. Even though we have used the highest ab initio electronic level reported up to now for dynamics calculations on these reactions, and although our results are quite good, we still do not match exactly the available experimental data. From our results it can be inferred that, probably, an adiabatic energy maximum between the CCSD(T)-SAC//MP2/cc-pVTZ and CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ values (5.6 and 6.2 kcal/mol, respectively, for the perprotio reaction) could be the most feasible, and that the description of the adiabatic profile fails especially in that region away from the transition-state location but crucial for tunneling corrections. (C) 2001 American Institute of Physics.