Abstract: The invention relates to an apparatus and a method for the treatment of the blood in a Continuous Renal Replacement Therapy, using a machine which comprises: —connecting means from and to respective blood vessels of a patient; —blood processing means comprising a pump; —means for adding drugs or other therapeutic substances to the blood being treated; —means for feeding refill liquid into the blood; —blood filtration means, cascade-connected to one another by relative conduits, said conduits and said connecting means defining a blood path; wherein the blood to be treated passes through an oxygenating device which comprises an oxygenating membrane and is located upstream from said blood filtration means and downstream from said blood processing means, so that the blood is treated by said oxygenating membrane without the intake pressure along the portion upstream from the blood pump; and wherein the blood is pumped downstream from the connecting means to the oxygenating device at a flow rate of about 280-300 ml