NOVELTY - The chemisorptive-catalytic purification of biogas, in particular, by a chemisorptive-catalytic system for purification of the biogas comprises the stirring device (1)of the source biogas with the air and the part of the biogas purified from sulfur; the heater of the produced gas mixture (2); the reactor of oxidation of hydrogen sulfide (3); the heat exchanger for cooling of the gas mixture and condensation of the vapors of the formed elemental sulfur (5); the pipeline (8) for recirculation of the part of the biogas purified from sulfur; and, at least two parallel chemisorbers (6) with the fixed layers of the solid granular chemisorbent of the hydrogen sulfide (7). The reactor contains the fixed layer of the solid granular catalyst (4) for oxidation of hydrogen sulfide by oxygen up to the elemental sulfur. The device stirring device contains the control system of the air consumption and the part of the biogas purified from sulfur made with the capability to maintain the concentration of hydrogen sulfide in the produced gas mixture of no more than 1.2 volumetric % and the concentrations of oxygen within the range of 60-100 % from the indicated concentration of the hydrogen sulfide. The invention allows to reduce consumption of the chemisorbent and the volume of formation of the secondary wastes, to utilize the biogas with production of power and commercial products - the elemental sulfur, the high-quality carbon dioxide and to increase efficiency of purification of the biogas at the minimal capital expenditure and the operational costs.    USE - Different branches of economy; the systems for purification of the biogas.    ADVANTAGE - The invention ensures: the reduced consumption of the chemisorbent and the volume of formation of the secondary wastes;, utilization of the biogas with production of power and commercial products - the elemental sulfur, the high- quality carbon dioxide; the increase efficiency of purification of the biogas at the minimal capital expenditures and the operational costs.