The invention relates to the monitoring of the fluid flow in an apparatus for extracorporeal blood treatment. The device according to the invention and the method according to the invention are based on the fact that, in order to monitor the fluid flow, the change in weight of a collection container is monitored, in which a rinsing fluid is collected during a filling or rinsing phase. The monitoring of the fluid flow according to the invention permits continuous monitoring of the fluid flow both in a treatment mode, in which the blood treatment is carried out, as well as in a filling or rinsing mode, in which the fluid system is filled or rinsed with a fluid.