Anaesthesia machine arrangement and a method in connection with an anaesthesia machine arrangement comprising a gas dispenser of an anaesthesia machine connected to a patient circuit that comprises a monitor device, a control device and an interface unit. The gas dispenser is configured to deliver a desired concentration of fresh gas to the patient circuit, the desired concentration being set by using the interface unit. The monitor device is configured by using a sample line to monitor gas concentration in the patient circuit and the control device is configured to control the gas dispenser from the basis of the data received from the monitor device to keep the desired fresh gas concentration.