EVALUATION OF THE RENAL FUNCTION: For the follow-up of the graft renal function it must be measured the glomerular filtration rate by means of formulae that use the serum creatinine. The most used equation is the brief formula MDRD. - All patients transplanted must be included in the group of Renal Chronic Disease though the glomerular filtration rate is normal and there is no evidence of renal damage. - The measures of intervention proposed in the classification of the Renal Chronic Disease for its progressive establishment in the stage 1 to 3, must be applied to all the transplanted THE BEGINNING OF DIALYSIS: In spite of receiving attention of Nephrologists along the whole evolution, the patients with chronic dysfunction of the graft that need treatment with dialysis start later and with more uremic complications that the patients who start dialysis for the first time. - To change this trend, it is necessary to consider the treatment with dialysis when the glomerular filtration rate is lower than 15 ml/min/1,73 m2. If there appears any complication related to the uremia that cannot be handled by conservative treatment, the beginning of the dialysis is necessary. THE BEGINNING OF THE DIALYSIS OF PROGRAMMED FORM: The beginning of the dialysis of not programmed form in transplanted patients is difficult to justify if we take into account that such patients, have received nephrological attention along all their evolution. - To get a new vascular access in these patients can be difficult depending on the previous trombosis of arteriovenous fistulas. Therefore, it must be realized a prompt evaluation for de department of vascular surgery to guarantee a suitable vascular access. - As general norm, one must follow the same criterion advised for the not transplanted patient: the vascular access must be considered when the glomerular filtration rate is lower than 20 m/min/1,73 m2. - The patient who is going to be treated by dialysis peritoneal precise a very narrow follow-up to be able to programme the placement of the catheter peritoneal with a minimum of 15 days before beginning the training.