Anaesthesia ventilator for the automated ventilation of a patient, having - an expiratory port and an inspiratory port for the attachment of a ventilation tube directed towards the patient and supplying a breathing gas, - a breathing gas delivery unit, - at least one volume flow sensor for detecting a volume flow of the breathing gas, at least one breathing gas sensor for detecting a carbon dioxide concentration, and at least one pressure sensor for detecting a pressure of the breathing gas, - and moreover at least one computer, which is configured, in a first mode of operation, to actuate the breathing gas delivery unit as a function of a pre-set ventilation rate, the detected pressure and a pre-set desired pressure value (Pinsp), wherein the computer is moreover configured - to detect, in the first mode of operation, the presence of a desired operating state concerning the automated ventilation, on the basis of the detected volume flow and of the detected carbon dioxide concentration, and, - upon detection of the operating state, to permit a change-over to a second mode of operation in which the computer actuates the breathing gas delivery unit in such a way that a pressure control ventilation or a pressure support ventilation is carried out, characterized in that the computer is configured, in the first mode of operation, - to determine, on the basis of the detected volume flow, a tidal volume delivered to the patient, - and moreover to determine an end-expiratory carbon dioxide concentration (etCO2) on the basis of the detected carbon dioxide concentration, and moreover to effect an adaptation of the desired pressure value (Pinsp) and an adaptation of the ventilation rate as a function of - the determined tidal volume, - an upper volume limit value, - a lower volume limit value, - the determined end-expiratory carbon dioxide concentration (etCO2), - an upper concentration limit value (etCO2O1), - and a lower concentration limit value (etCO2U1). - an expiratory port and an inspiratory port for the attachment of a ventilation tube directed towards the patient and supplying a breathing gas, - a breathing gas delivery unit, - at least one volume flow sensor for detecting a volume flow of the breathing gas, at least one breathing gas sensor for detecting a carbon dioxide concentration, and at least one pressure sensor for detecting a pressure of the breathing gas, - and moreover at least one computer, which is configured, in a first mode of operation, to actuate the breathing gas delivery unit as a function of a pre-set ventilation rate, the detected pressure and a pre-set desired pressure value (Pinsp), - to detect, in the first mode of operation, the presence of a desired operating state concerning the automated ventilation, on the basis of the detected volume flow and of the detected carbon dioxide concentration, and, - upon detection of the operating state, to permit a change-over to a second mode of operation in which the computer actuates the breathing gas delivery unit in such a way that a pressure control ventilation or a pressure support ventilation is carried out, - to determine, on the basis of the detected volume flow, a tidal volume delivered to the patient, - and moreover to determine an end-expiratory carbon dioxide concentration (etCO2) on the basis of the detected carbon dioxide concentration, and moreover to effect an adaptation of the desired pressure value (Pinsp) and an adaptation of the ventilation rate as a function of - the determined tidal volume, - an upper volume limit value, - a lower volume limit value, - the determined end-expiratory carbon dioxide concentration (etCO2), - an upper concentration limit value (etCO2O1), - and a lower concentration limit value (etCO2U1).