Inclusion Criteria:

- Patients will be eligible if their primary indication for transplantation is among
the following: Indolent B-cell non-Hodgkin lymphoma (NHL); Aggressive B-Cell NHL;
T-cell NHL; or Hodgkin Lymphoma.

- Patients must have one of the following combinations of disease status and disease
histology at the time of enrollment: 1) Patients may be transplanted as part of
first-line therapy if they have one of the following histologies: CLL with adverse
cytogenetics, MCL or, T-cell NHL. 2) Patients may be transplanted as part of
treatment for relapsed or refractory disease without a prior autologous
transplantation of they have one of the following histologies: Indolent NHL
(including CLL/SLL), MCL or T-cell NHL. 3) Patients may be transplanted as part of
treatment for disease that has relapsed or progressed after autologous
transplantation if they have any of the histologies listed above. Patients may also
be enrolled without a prior autologous transplantation if they have a
contraindication to autologous transplantation, in the opinion of the treating
clinician. 4) There is no minimal or maximal time interval from the patient's last
anti-lymphoma therapy and the time of transplantation.

- 18-72 years of age

- Matched related or matched unrelated donor

- Donor willing to donate peripheral blood stem cells and meeting institutional
criteria for stem cell donation. The donor must be medically eligible to donate stem
cells according to individual transplant center criteria.

Exclusion Criteria:

- Patients with Burkitt lymphoma or DLBCL with a c-myc rearrangement

- Karnofsky performance status of less than 70% at the time of registration

- Prior allogeneic stem cell transplantation (note that prior autologous stem cell
transplantation is allowed)

- Uncontrolled infection

- Serum creatinine 2.0mg/dl or greater

- Total bilirubin 2.0mg/dl or greater (unless related to hemolysis or Gilbert's
syndrome)

- Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) 3 times or greater
than the institutional upper limit of normal

- Left ventricular ejection fraction < 30%

- Cholesterol > 500mg/dl or triglycerides > 500 mg/dl despite appropriate treatment

- Seropositivity for HIV

- Pregnancy or breast-feeding (effective contraception must be used during therapy and
for at least 6 months after the end of immunosuppressive agents)

- Prior history of allergy to sirolimus, tacrolimus, cyclosporine, methotrexate or MMF

- Concomitant treatment with another investigational drug (unless cleared by study
chair)