The objective of this paper is to develop material balances, equilibrium, and transport equations for a binary gas mixture separation in the single-membrane and two-membrane cascades, and to compare their performances. An analysis is restricted to the case of zero permeate pressures, symmetric separation effects and perfect mixing conditions in each stage. The governing sets of equations are analytically solved in order to obtain the membrane area requirements, and interstage flowrates and concentrations as functions of the feed flowrate and composition, the total number of stages, the position of the feed stage, the upstream pressure, and the membrane selectivities and specific permeabilities. The graphical procedures for obtaining the required number of stages are also developed. The simulation results are presented for the CO2/H-2 separation using silicone rubber and CA membranes.