The hypothesis of this study is that lymphocyte depletion by Campath-1H and rituximab will obviate the need for long-term calcineurin inhibitors in renal transplantation. Most successful strategies to date have relied on the use of either tacrolimus or cyclosporine. However, the advantage of a calcineurin inhibitor free regimen may include improved renal allograft function, a lower incidence of hypertension, diabetes, and less drug related side effects. This is a non-randomized open-label pilot trial in 30 adult renal transplant patients.