FIELD : medicine.SUBSTANCE : invention relates to medicine, namely to oncology, and can be used for the treatment of cancer. For this purpose, inhalations are performed using gaseous mixtures of oxygen and a noble gas of argon. Treatment is carried out with the content in the used gas mixture of oxygen in an amount of from 12 to 20?%. Time of one procedure is 5–20 minutes. Total inhalation time per day is at least 80 minutes. Inhalation is performed with the use of the breathing circuit with the purification of carbon dioxide with a total flow rate of the gas mixture of at least 1 l/min in a semi-open or semi-open circuit.EFFECT : method provides treatment of oncological diseases with low degrees of malignancy due to an increase in the oxidation process inside tumor cells due to an increase in their mitochondrial and microsomal oxidation.3 cl