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 Rel-B/ NFkB pathway thus preventing monocyte and macrophage activation. Extensive preliminary data have been accumulated in humans using Campath-1H and its non-humanized predecessors. Additionally, data have been generated using a similar depleting scheme with and without DSG in non-human primates. Both the human and non-human primate data suggest that profound mature mononuclear cell depletion establishes a window of opportunity during which foreign tissue can be transplanted without the need for additional immunosuppression. Regulatory events occuring during mature cell repopulation in the presence of allografted tissue created a state in which the graft may not be rejected even in the absence of chronic immunosuppression.