A description is given of a method of monitoring the operationality of a flow cut-off member for an extracorporeal fluid circuit. Also described is a system for arresting the flow of blood that implements this monitoring method. The system has a flow cut-off member active on a radially deformable length of tube forming part of the circuit, and a unit capable of causing a movement of a movable portion of the cut-off member towards a closed condition. The system detects when the movable portion passes through a first predetermined position and determines the value assumed by a dynamic parameter associated with the motion of the movable portion at the first predetermined position. The system further checks that this value is within a predetermined criterion of acceptability. Lastly, a blood treatment appliance is described that implements the described method and system.