Abstract: The invention relates to an appliance for performing anaesthesia or analgosedation, comprising a dosing device (5) for the intravenous administration of an adjustable dose of at least one anaesthetic to a patient (1), a measuring device (2) for determining the concentration of the at least one anaesthetic in the exhaled air of the patient (1), means (4) for determining the effect of the at least one anaesthetic on the patient (1), preferably in the form of a depth of anaesthesia or depth of analgosedation, and a data processing device (7), which communicates via interfaces with the dosing device (5), the measuring device (2) and the means (4) for determining the effect and which, on the basis of the determined values of the parameters dosage, concentration and effect of the at least one anaesthetic, establishes a pharmacological model individualized to the patient (1) and, using the individualized pharmacological model that is established, calculates an individual dosage, optimized to the patient (1), of the