The invention relates to a method and a device for monitoring an extracorporeal blood circuit I during an extracorporeal blood treatment using an extracorporeal blood treatment device. The invention further relates to an extracorporeal blood treatment device with a device for monitoring an extracorporeal blood circuit. The method according to the invention and the device according to the invention are based on carrying out the monitoring process of the arterial and/or venous access to the patient using a first and a second method in order to increase the redundancy, wherein the presence of at least one criterion characterizing an incorrect state of the vessel access is checked in each method, the criteria of the first and second methods being different from one another. In the method according to the invention and the device according to the invention, the blood pump (9), which is preferably an occluding blood pump, is stopped after the presence of the at least one criterion of the first method is ascertained, whereas the venous closure element (17) remains open, however. The presence of the at least one criterion of the second method is checked after the blood pump (9) has been stopped. The venous closure element (17) is closed only if the at least one criterion of the second method is present. Otherwise, the blood pump (9) is restarted in order to continue the blood treatment.