The invention relates to an arrangement (200) for anaesthetising a living creature (V) and for maintaining said creature in an anaesthetised state, by administering thereto an infused volume of anaesthesia inducing pharmaceutical (22) in liquid phase per unit of time, with the aid of one or more lung ventilator units (A) and one or more infusion units (B). Chosen parts of the lung ventilator unit, with the exception of external insufflation hose, expiration valve, measuring probe and a number of hoses (12), and selected parts of the infusion unit (B), with the exception of cannula (5B) and hose (4B) are mutually combined to form a single equipment unit (201). Some of the parts of the equipment unit are mutually coordinated with respect to communication via a computer unit (600) included in the equipment unit, and the computer unit is adapted to monitor unit related criteria and creature related criteria.