Single-cascade simulated moving bed (SMB) systems with a side-stream withdrawal are developed for separating ternary systems. Several single-cascade SMB systems are studied for the separation of ternary mixtures within the linear range. Design parameters, operating conditions, minimum desorbent-to-feed ratios, and productivities are determined with the local equilibrium theory, and purities are determined through detailed Aspen Chromatography simulations. A series of initial feed compositions are simulated to determine the optimal regions. The single-cascade SMB is particularly applicable when there is little of the most strongly adsorbed component, a significant amount of the middle component, and the separation between these components is easy. A surprising finding is that the purity of the middle-component product is usually higher in an SMB than in a true moving bed. A few quaternary separations with a side-stream SMB followed by a binary SMB are also studied.