To minimize the effect of rejection in transplantation takes into account the compatibility between donor and recipient, taking into account blood group and HLA system. Anyway, then the person receiving the transplant must receive immunosuppressive drugs to prevent the body is recognized as foreign and a rejection occurs, except in the case of isotrasplantes. The effect of rejection is caused by a very simple fact: every living organism defends its physical and biochemical destroying any strange living agent that has been introduced into it. Likewise the body has certain proteins characteristic of their genetic code that are specific to each human being (except for the twins, who have the same genetic codes).Therefore, the body, to be invaded by antigens (protein substances), reacts with a natural defense motion, rejecting the trasplante.Para avoid the rejection, the patient must be applied drugs and treatments, with the disadvantage that the patient loses full immunity. In August 2008, successfully performed the kidney tranplante cross between patients of different race, to avoid incompatibilities makes use of plasmapheresis method by which blood is removed from the antibodies that can cause the implanted organ rejection.