This protocol facilitates the development of methods for determining whether transplant recipients have developed immune hyporesponsiveness or tolerance towards their allograft. These methods will involve the study of peripheral blood or biopsy tissue obtained at regular intervals from patients receiving kidney or combined kidney-pancreas allografts at the NIH Clinical Center. In addition, patients that have previously received a kidney or combined kidney-pancreas allograft will be evaluated using assays requiring peripheral blood mononuclear cells and/or biopsies. Assays developed under this protocol will be used in subsequent protocols to assess the effects of immune modulating treatment regimens and may eventually be used to direct clinical care or guide the withdrawal of immunosuppressive agents. However, patients enrolled in this protocol will not have any change in treatment based solely on the assays developed without being enrolled in an additional study.