By establishing the renal suppletion procedure, the patients with chronic renal failure also have an acceleration of arterial hypertension phenomena. The management of this situation calls for the understanding of the ethological mechanisms (hypervolemia by the reduction of Na excretion and high rennin secretion) and the adaptation of the therapeutic approach to every patient. An individualized dialysis prescription is imposed, taking into account the residual renal function and an anti–hypertension treatment, in which the role of the conversion enzyme inhibitors (ACE inhibitor) is intensely debated.