An insufflation system has a medical instrument, which has a channel through which an insufflation gas can be passed from the proximal end to the distal end. A first valve in the instrument can be switched between a first switching state and a second switching state. It is proposed that a pressure sensor be provided which is connected to the channel and which can detect the two switching states of the first valve. A second switch-over valve can be switched by a control unit in accordance with the detected pressure values, such that the instrument can be connected by the second switch-over valve either to a source of insufflation gas or to a source of air. The second switch-over valve is designed such that only air is delivered in the first switching state of the first valve and only insufflation gas is delivered in the second switching state.