This paper presents a mathematical model of the transient behavior of the hydrodynamics of a countercurrent packed-bed column. The model has been solved numerically for two conditions representing a step increase of either gas or liquid inlet velocity. The obtained profiles exhibit overshoots of pressure drop and liquid holdup for conditions when the step change brings the system into the region where liquid holdup is also a strong function of gas velocity. This fully confirms our previous observation of pressure drop and liquid holdup overshoots when the system is brought into the proximity of the flooding point where this condition is satisfied. Our results show that the overshoots appear as a result of the formation of a new liquid holdup profile that temporarily lowers the liquid velocity in the lower parts of the bed while it temporarily increases the gas velocity in the upper parts of the bed. Reasonable agreement was found between the predicted and experimental transient profiles of pressure drop and liquid holdup exhibiting overshoots.