An extracorporeal alarm suppression method is arranged to be carried out in a continuous renal replacement therapy and/or chronic hemodialysis device and includes the steps of monitoring vascular access pressure, including arterial and/or venous pressure, of a patient using a vascular access pressure monitoring means； detecting an access pressure alarm situation if the arterial or venous pressure is out of predetermined alarm limits； when a first access pressure alarm situation is detected, setting the device to an alarm suppression state reducing the blood flow and therapy flows using an alarm suppression state setting means； detecting that a predetermined alarm suppression state condition is met using a predetermined alarm suppression state condition detecting means, the predetermined alarm suppression state condition including at least a predetermined waiting time having passed or a parameter threshold having been reached after the first access pressure alarm situation has been detected； and when a further access pressure alarm situation is detected after the predetermined alarm suppression state condition has been met, setting the device to a safety state using a safety state setting means, the safety state being a state in which the blood pump is stopped.
