FIELD: medicine.SUBSTANCE: group of inventions relates to medicine and to medical equipment, namely to a method of producing therapeutic gas mixtures and a method for training patients with therapeutic gas mixtures. Proposed method comprises feeding atmospheric air into gas separation element. Atmospheric air is mixed with air exhaled by the patient, compressed and supplied to the first hollow-fiber gas separation element, where the gas mixture enters the intrafibre or interfibre space. First gas flow penetrating through the membrane wall forms a hyperoxic mixture with a hypercapnic component. Second flow of gas not penetrated through the membrane forms a hypoxic mixture. Third gas flow, which is part of the gas flow penetrating through the membrane wall, is compressed and directed to the second hollow-fiber gas separation element, where the gas mixture enters the intrafibre or interfibre space. Fourth flow of gas not penetrated through the membrane wall of the second hollow-fiber gas separation element is recycled to the inlet into the first hollow-fiber gas separation element. Fifth flow of gas penetrated through the membrane is mixed with the sixth flow – a portion of the gas flow not penetrated through the wall of the membrane of the first hollow-fiber gas separation element, and forms a hypoxic mixture with a hypercapnic component. Method of training patients with therapeutic gas mixtures involves alternate delivery of mixtures to patients in respiratory training procedures. Each procedure consists of 3–15 cycles of exposure of patients to therapeutic gas mixtures. One cycle represents exposure to hypoxic mixture or hypoxic mixture with hypercapnic component for 1–30 minutes. That is followed by exposure to a hyperoxic mixture with a hypercapnic component for 1–30 minutes. Every 3–5 procedures, the carbon dioxide content in the cycle mixtures increases by 0.5–1 % and the oxygen content in the hypoxic mixture or the hypoxic mixture with the hypercapnic component
