An apparatus (100) for extracorporeal blood cleaning includes a separation unit (110), at least two processing branches (120; 130) and a mixing unit (140). The separation unit (110) receives 5 incoming blood (B A) and divides off a first fraction (fC) from this blood. The first fraction (fC) contains predominantly blood cells. The separation unit (110) also divides off at least one second fraction (fP), which contains predominantly blood plasma. A first processing branch (120) processes the first fraction (fC) according to a first cleaning process, in which cell-bound substances are removed from the blood cells. As a result, a first cleaned fraction (fC c) containing washed blood cells is produced. A second processing branch (130) processes the second fraction (fP) according to a second cleaning process in which toxins bound on proteins within the plasma and/or toxins dissolved in 15 the plasma are removed, and a second cleaned fraction (fP c) is produced. The second cleaning process is different from the first cleaning process. Thereby each process can be tailored for the requirements of the respective fraction (fC, fP). The mixing unit 20 (140) receives the first and second cleaned fractions (fC c, fP c, combines these fractions (fC c, fP c, and outputs cleaned whole blood (BV).