In a hemodiafiltration apparatus, a control and command unit (11) halts a replacement fluid supply pump (8) and contemporaneously modifies the control mode of a blood pump (1) passing from a control based on the pump velocity to a control based on the blood pressure measured by a sensor (12) arranged downstream of a hemodiafilter (3). The aim is to prevent risks due to excessive hemoconcentration in the blood circuit between the ultrafiltration zone and the infusion zone.