This protocol will test a humanized monoclonal antibody known as Campath-1H for its ability to induce a state of permanent allograft acceptance, or tolerance, when administered in combination with a brief course of the immunosuppressive drug deoxyspergualin (DSG) at the time of human renal allotransplantation. Campath-1H is specific for the common lymphocyte and monocyte antigen CD52. Its administration temporarily depletes mature lymphocytes and some monocytes without altering neutrophils or hematopoietic stem cells. Deoxyspergualin inhibits the NFkB pathway thus preventing monocyte and macrophage activation.