Simulated Moving Bed separations of enantiomers or fine chemicals are usually carried out in the isocratic mode, i.e. by applying the same operating conditions (temperature, pressure, mobile phase composition, pH) in the whole SMB unit. However, it has been recently recognized that by properly modulating operating conditions in the SMB sections. i.e. Sections 1-4 normally, separation performance in terms of productivity and solvent consumption can be significantly improved. In this work, we study solvent gradient SMB (SG-SMB) operation, where the concentration of a modifier in the main solvent constituting the mobile phase is adjusted along the SMB unit, so as to have weaker retention of the species to be separated in the first two sections, and stronger retention in Sections 3 and 4. Overload chromatographic conditions are considered, where the adsorption behavior is characterized by a nonlinear competitive adsorption isotherm, e.g. a binary Langmuir isotherm. Design criteria to achieve complete separation are developed in the frame of the equilibrium theory of chromatography. The theoretical findings are discussed in view of typical effects of the modifier concentration on retention times and solubility of the species to be separated, and an overall assessment of the SG-SMB technology is attempted.