The invention relates to a device and to a method for monitoring access to vessels during extracorporeal blood treatment. The invention forms a loop in the arterial and/or venous line and provides device for fixing a section of the line in a loop. When the line is stressed under tension, the loop contracts and the line finally kinks. The modification of the diameter of the line and the formation of a kink in the line leads to a rise of pressure in the line, which is monitored by a pressure monitoring device. If the pressure exceeds a predetermined threshold value, the aspirating cannula is in danger of slipping out of the vessel access or has partially or completely slipped out, thus allowing the threshold value to be determined for alarms.