The wave approach to the description of periodic processes of adsorption and desorption allows to consider different adsorption technologies of gas mixtures separation from the same positions. The description of mathematical modeling of a relatively new adsorption technology for the gas mixtures separation known as Dual Piston Pressure Swing Adsorption System has been presented. The main advantage of DP-PSA-technology is practically complete separation of the two-component mixture in the installation with a single adsorber and a significant reduction of energy consumption for the separation of the gas mixture. The analysis of the adequacy of the mathematical model to the real processes after the example of the system optimization for obtaining oxygen from the air has been made. When optimizing the system the target function is the concentration of the produced oxygen. As the optimized parameters the following have been chosen: the phase-shift angle of the pistons motion and the ratio between the volumes made by the pistons. The phase of the piston motion in the cylinder filled with air passes ahead by 51° the piston motion in the cylinder filled with the produced oxygen. In this case the concentration of oxygen at the outlet of the installation reaches 94.7%. The optimum ratio of the volume made by the pistons turned out to be one.