A method and a device for recognition of paravasal bleeding upon a supplying of blood to a vascular access via a line and/or upon the removal of blood from a vascular access via a line is provided. A device for extracorporeal blood treatment comprising a device for recognition of paravasal bleeding is also provided. The method and the device are based on the change of arterial pressure in the arterial branch or the venous pressure in the venous branch of the extra-corporeal circuit being registered during the extracorporeal blood treatment. One aspect of the method and the device is that pressure changes that come from a pressure level exhibiting a large difference from a reference value are more strongly considered than those that come from a pressure level that exhibits only a minor difference from the reference value.