Mathematical equations have been formulated to predict the longitudinal concentration distribution in the case of instantaneous behavior of a continuous chromatographic system. Partial differential equations are initially obtained from mass balance on the differential element of column height. The formulated equations are solved by Laplace transformation and the contour integration method. Two equations are obtained, one for the column section above the feed point and the second for the column section below the feed. Both of these equations give the concentration distribution along the appropriate section of the column. The model predicts the instantaneous and steady-state behavior of the continuous moving-bed chromatographic system. The model can also be used as a tool for the design of new continuous chromatographic columns.