The effect of the nondiffusional short-time liquid dynamics on the kinetics of an irreversible bimolecular solution reaction (A+B-->products) is investigated using a non-Markovian Smoluchowski approach. It is shown that due to the convolution-type basic equation in this concept, asymptotic rate coefficient predictions can be deduced from exact results of the Smoluchowski-Collins-Kimball theory. For the case that only the inertial effect plays a significant part in the nondiffusional reactant pair dynamics, an asymptotic short-time expansion of the rate coefficient was derived in this way. It explicitly indicates as a new reaction-kinetic result how the rate coefficient in the short-time region depends on the AB potential of mean force. Specified for the conditions of contact reactions in a simple hard-sphere fluid, the kinetic predictions of the new concept are compared with the results of other approaches. (C) 2003 American Institute of Physics.