The invention relates to a process for monitoring the supply of substitution fluid upstream or downstream of a dialyser or filter arranged in an extracorporeal blood stream. One embodiment provides, for the detection of predilution or postdilution, for measuring the pressure in the blood stream downstream of the dialyser or filter, predilution or postdilution being recognized on the basis of the change in pressure following the shutting off and/or starting up of the substituate pump provided for conveying the substitution fluid. Another embodiment provides for recognizing predilution or postdilution on the basis of the comparison of the oscillating pressure signal attributable to the substituate pump to a characteristic reference signal. The characteristic reference signal to which the pressure signal of the substituate pump is compared is preferably the oscillating pressure signal of a blood pump arranged in the blood stream for conveying the blood upstream of the dialyser or filter. In addition, the invention relates to an extracorporeal blood treatment device with a facility for detecting predilution or postdilution, which device operates according to the processes detailed above.