The present invention relates to a moisture detection system which takes the form of a covering to be applied to the patient's skin, and to a monitoring system for monitoring a vascular access for a blood-treating apparatus. The covering of the moisture detection system has a flexible substrate material to which an electrically conductive structure having printed conductors is applied as a moisture sensor. In accordance with one aspect of the present invention, because a terminating resistor is not part of a moisture detection system, the device can be inexpensively produced in large quantities. This is of advantage in that the moisture detection system is generally intended for once-only use. With the separate terminating resistor, there is no risk of the terminating resistor being damaged or its resistance changing due to movements on the part of the patient.