Abstract: The method comprises the stages of a) setting the ventilatory rate (VR) for the patient; b) automatically setting the flow of fresh gas (FFG) to 10% of the VR; c) determining the volatile anaesthetic fractions inhaled (% IF) and exhaled (% EF); d) opening the dial of the anaesthetic vaporiser to the value resulting from multiplying the differential (% IF−% EF) by 10; e) supplying the circuit with a quantity of anaesthetic that covers, at least, the total quantity of anaesthetic consumed by the patient, by means of opening the dial of the anaesthetic vaporiser; and f) mixing the quantity of anaesthetic with the FFG before introducing the mixture into the patient. The method has application in the administration of inhaled anaesthetics in low-flow anaesthetic systems.