A mathematical model for a simulated moving bed adsorption system is presented using a more precise approach. In this precise approach the differential equations along with appropriate boundary conditions are written for each adsorption column as distinct from the section approach adopted by previous workers in order to examine the column dynamics of the actual system. An axially dispersed plug flow model with linear driving force rate expression for mass transfer and nonlinear Langmuir equilibria are considered. The time-dependent boundary conditions for each column are formulated and related to switching time. Computations are performed for several cycles till the cyclic steady state is reached. The results obtained from the present model for the limiting cases of linear glucose-fructose and nonlinear monoethanolamine-methanol systems are compared with available experimental data and are found to agree well. The effect of various process parameters on the performance of systems are investigated and the distinction from the section approach is emphasized. The present study reveals that the system performance and dynamics are strongly dependent on axial dispersion, eluent-to-feed ratio, bed length and switch time. It is observed that there exists a set of optimum values of all the parameters for best process performance, which can be evaluated from the present simulation.