An apparatus and a method for monitoring the supply of replacement fluid during an extracorporeal treatment of blood is disclosed. Detection of the supply of replacement fluid upstream or downstream of the dialyser or filter is based on a measurement of the optical or physical density of the blood or of a constituent of blood in the extracorporeal circulation. To detect pre- or post-dilution, the blood flow rate and/or the replacement rate and/or the flow rate of the fluid removed from the blood through the dialyser membrane is altered, and the density of the blood or of the constituent of blood is measured upstream and/or downstream of the dialyser. Additionally, an apparatus for treating blood with an apparatus for monitoring the supply of replacement fluid is disclosed.