The present calculations represent the first theoretical study of the mechanism of the reactions Cl + HOCl --> products (R1) and H + HOCl --> products (R2). A direct dynamics method is employed to perform the dynamics calculations of the two reactions. Optimized geometries and frequencies of all of the stationary points and extra points along the minimum-energy path (MEP) are obtained at the MP2/6-311+G(2d, 2p) level of theory. For the system of HOCl with Cl atoms, two complexes with energies less than that of the reactants are located in the reactant channel of the Cl abstraction and H abstraction. The energy profiles of two the reactions are refined with the interpolated single-point energy (ISPE) method at the G3//MP2 level. The rate constants are evaluated using the improved canonical variational transition-state theory (ICVT) with a small-curvature tunneling correction (SCT) over a range of temperatures from 220-2000 K. Agreement between the ICVT/SCT rate constants and the experimental values is good. Our calculations show that in the low-temperature range the branching ratio to the hydrogen abstraction channel for the two reactions is negligible, and the reactions proceed practically via chlorine abstraction, leading to the formation of OH + Cl-2 and OH + HCl, respectively; for the reaction Cl + HOCl, the hydrogen-abstraction channel appears to be probable as the temperature increases. Furthermore, the calculated rate constants are also consistent with the study of the reverse reaction OH + Cl-2 --> Cl + HOCl. The tunneling correction has an important contribution in the calculation of rate constants in the low-temperature range.