The dynamics of adsorption of Kr and Xe, which are constituents of the off-gas from the nuclear reprocessing process, on representative adsorbents (MS5A and activated charcoal) was studied using packed bed columns. The experimental breakthrough curves were analyzed by conducting direct numerical computations of the mass balance equations. The results of the analysis show that adsorption of Kr and Xe on the MS5A adsorbent is the pore diffusion control. With regard to the adsorption of Kr and Xe on the activated charcoal, it was found that the surface diffusion considerably contributes to the migration of adsorbate molecules. These results suggest that the kinetic adsorption performance of the activated charcoal adsorbent is enhanced even at lower temperatures with the help of the surface diffusion. Furthermore, the surface diffusivities were quantified from the experimental results using several models.