Abstract: A device is disclosed which comprises at least one sleeve having a number of chambers. The sleeve may be placed around the patient's extremity which is to be treated, and the chambers can be inflated and deflated by means of valves. To accomplish an optimum treatment of the patient and an uncomplicated construction of the device, all the valves are connected in series and arranged to be operated successively in cascade-fashion via common feed and control pipes which are connected only to the first valve, whilst downstream each pair of mutually adjacent valves are interconnected via sections of feed and control pipes. In each valve a valve member such as a diaphragm separates a supply volume of the valve, which is in constant communication with an infeeding feed pipe section and with the assoicated chamber, from a valve control volume which is in constant communication with the control pipe.