Reactive chromatographic processes are investigated theoretically for irreversible A -> B and reversible A <-> B reactions. The models consist of two partial differential equations, accounting for each component convection, longitudinal dispersion, adsorption, and first-order chemical reactions. Analytical and numerical solutions of the models are needed for analyzing and optimizing the processes in the fixed-bed column. Analytical solutions are obtained by means of Laplace transformation. Temporal moments are derived from the Laplace-transformed solutions. For validation, the high-resolution upwind finite volume scheme is applied to solve the model equations numerically. Several case studies are carried out, and the analytical solutions are compared with the numerical ones. The good agreement between solutions verify both the correctness of the analytical solutions and the accuracy of the suggested numerical scheme.