A continuous renal replacement therapy (CRRT) apparatus for CRRT of the type performable using a hemofiltration machine, has an oxygenating device. A continuous renal replacement therapy apparatus for CRRT of the type performable using a hemofiltration machine, comprises connecting mechanisms (9, 9) from and to respective blood vessels of a patient a blood processing mechanism comprising a pump (3) an addition mechanism for adding drugs or other therapeutic substances (5) a feeding mechanism for feeding refill liquid into the blood (6) a blood filtration mechanism (8) cascade-connected to one another by relative conduits and an oxygenating device (7).