The device controls a system (20) for transporting blood and which is controlled so that the blood in the blood line is transported in a pre-determined volume flow as long as the pressure in the blood line (9) is below the pre-determined threshold value. When the pressure in the blood line (8) reaches the pre-defined threshold value, a pressure value (27) corresponding to the threshold value is set when the blood is transported. When the threshold value for the pressure is reached, a regulation of the volume flow is replaced by a regulation of the pressure in the blood line. An independent claim is included for a method for transporting blood in a blood line of an extra corporeal blood circuit of an extra corporeal blood treatment device.