Mathematical models of dynamics of pressure swing adsorption processes for the separation of synthesis gas (into hydrogen, carbon dioxide and carbon monoxide) and air (into oxygen, nitrogen and argon) have been developed. The models allow calculating the profiles of component concentrations and temperature of gas and solid phases, pressure and velocity of gas mixture along the height of adsorbent in relation to time. The models include the following equations: 1) processes of mass and heat transfer during the adsorption (desorption) of a sorptive (H 2 , CO 2 , CO and O 2 , N 2 , Ar) by granulated zeolite adsorbents 5A and 13Х; 2) kinetics of compound diffusion transport of adsorbate and Langmuir-Freundlich isotherm (for the synthesis gas separation), kinetics of external diffusion and Dubinin-Radushkevich isotherm (for the air separation); 3) the Ergun equation for the calculation of pressure and velocity of gas mixture in adsorbent. Using mathematical modeling the interrelation between the temperature, composition and pressure of the initial gas mixture and the purity, recovery ratio and temperature of the product gas (hydrogen and oxygen) has been established for a wide range of 'adsorption-desorption' cycle intervals and pressure during the adsorption stage. The dynamics of the adsorption of gas mixture components has been researched, as well as the nature of sorption and heat development over the height of adsorbent layer in the adsorber. The purity of the end product (hydrogen, oxygen) has been analyzed against the degree of productivity of a PSA unit. The paper presents formulations and solutions of optimisation problems for different regime variables (adsorption and desorption stage duration, pressure during adsorption and desorption stages, backflow coefficient) of the PSA unit with regard to the following criteria: 1) maximum purity (concentration) of the gas (hydrogen, oxygen) for a given productivity of the unit, 2) maximum productivity of the unit to meet the concentrated oxygen purity constraint.