A dispersion model developed in chromatographic theory is applied to the analysis of the elution profile in the liver perfusion system of experimental animals. The equation for the dispersion model with the linear nonequilibrium partition between the perfusate and an organ tissue is derived in the Laplace-transformed form, and the fast inverse Laplace transform (FILT) is introduced to the pharmacokinetic field for the manipulation of the transformed equation. By the analysis of the nonlinear least squares method associated with FILT, this model (two-compartment dispersion model) is compared to the model with equilibrium partition between the perfusate and the liver tissue (one-compartment dispersion model) for the outflow curves of ampicillin and oxacillin from the rat liver. The model estimation by Akaike's information criterion (AIC) suggests that the two-compartment dispersion model is more proper than the one-compartment dispersion model to mathematically describe the local disposition of these drugs in the perfusion system. The blood space in the liver, VB, and the dispersion number DN are estimated at 1.30 ml (+/- 0.23 SD) and 0.051 (+/- 0.023 SD), respectively, both of which are independent of the drugs. The efficiency number, RN, of ampicillin is 0.044 (+/- 0.049 SD) which is significantly smaller than 0.704 (+/- 0.101 SD) of oxacillin. The parameters in the two-compartment dispersion model are correlated to the recovery ratio, FH, mean transit time, tH, and the relative variance, sigma 2/t-2H, of the elution profile of drugs from the rat liver.