The goal of this clinical research study is to learn if fludarabine, melphalan and gemcitabine followed by transplantation of stem cells (blood-forming cells) as well as immune cells (lymphocytes), collected from a matched related (i.e. a sibling) or unrelated donor, or a mismatched related donor, can help to control Hodgkin's disease. The safety of the treatment will also be studied.

Central Venous Catheter:

If you choose to take part in this study, the chemotherapy, some of the other drugs in this study, and the stem cell transplant and immune cells will be given by vein through your central venous catheter (CVC). A CVC is a sterile flexible tube and needle that will be placed into a large vein while you are under local anesthesia. Blood samples will also be drawn through your CVC. The CVC will remain in your body during treatment. Your doctor will explain this procedure to you in more detail, and you will be required to sign a separate consent form.

Study Drug Administration:

The days before you receive your stem cells are called minus days, such as Day -2, Day -1. The day you receive the stem cells is called Day 0. The days after you receive the stem cells are called plus days, such as Day +1, Day +2.

On Day -7, you will receive gemcitabine by vein over about 40-180 minutes.

On Day -6, you will be admitted to the hospital and given fluids by vein to hydrate you.

On Days -5 and -4, you will receive fludarabine by vein over about 30 minutes.

On Days -4 and -3, you will receive thymoglobulin, if you are receiving a transplant from a matched unrelated donor (not a blood relative), a mismatched related donor (a blood relative, but not a full match), you will also receive antithymocyte globulin (ATG)

On Days -3 and -2, you will receive fludarabine by vein over about 30 minutes and melphalan over about 30 minutes.

On Day -1, you will "rest" (not receive chemotherapy).

On Day 0, you will receive the donor's stem cells and immune cells by vein. The infusion will last anywhere from about 30 minutes to several hours. You may be given other standard drugs to help lower the risk of side effects. You may ask the study staff for more information about how the drugs are given and their risks. All participants are expected to need blood transfusions as part of this treatment.

Beginning on Day -2, tacrolimus will be given by vein over 24 hours to help lower the risk of graft-versus-host disease (GVHD). This will be changed to pills once you can tolerate swallowing pills. If no active cancer is detected and there is no GVHD, you will then swallow 1 or more tacrolimus pills a day for only about 3-4 months, instead of the usual period of 6 months. This is done to boost the donor immune system against the cancer.

Starting 1 week after the transplant (Day +7), you will receive filgrastim (G-CSF) as an injection under the skin 1 time each day until your blood cell levels return to normal. Filgrastim is designed to make white blood cells grow, which may help to fight infections.

On Days +1, +3, +6, and +11, you will receive methotrexate by vein to decrease the risk of GVHD.

If you have persistent but stable (not "growing") disease after transplant, you will have your immunosuppressive medications (tacrolimus, corticosteroids) stopped even before 4 months. If there is no response, you will receive an infusion of additional cells from your donor.

Study Visits:

About 30 days before receiving the stem cells, you will have computed tomography (CT) and/or positron emission tomography (PET) scans to check the status of the disease.

About every day until discharge, and then at least weekly:

• You will have a physical exam.
• Blood (about 4 tablespoons) will be drawn for routine tests.

Follow-Up Visits:

About 100 days after the transplant:

• You will have a physical exam.
• Blood (about 4 tablespoons) will be drawn for routine tests. Part of the blood sample may be used for chimerism analysis (determination of donor or recipient cells), if needed.
• At any point that your doctor thinks they are needed, you will have a bone marrow aspiration, chest x-rays, and CT and/or PET scans to check the status of the disease. To collect a bone marrow aspirate, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow is withdrawn through a large needle.

About 6 months, 1 year, then annually after the transplant:

• You will have a physical exam.
• Blood (about 4 tablespoons) will be drawn for routine tests. Part of the blood sample may be used for chimerism analysis (determination of donor or recipient cells), if needed. Part of the blood will be used to check your thyroid function once a year.
• At any point that your doctor thinks they are needed, you will have a bone marrow aspiration, chest x-rays, and CT and/or PET scans to check the status of the disease.
• You may have lung function tests, if your doctor thinks it is needed.
• About 6 months after the transplant, you may have a biopsy, if your doctor thinks it is needed.
• About once a year, you will have an eye exam.

The above tests/procedures may be repeated more often, if you doctor thinks it is needed.

The study staff will also stay in contact with your local doctor to find out if the disease comes back and to check how you are doing.

Length of Treatment:

You will be on study for about 3 years. After 1 year, there is no study specific testing you will be required to complete. Your transplant doctor will perform routine standard of care follow-up that all patients receiving allogeneic stem cell transplantation receive.

You may be removed from the study early if the doctor thinks it is in your best interest, if the disease gets worse or comes back, if intolerable side effects occur, if you have graft failure (the transplanted cells do not grow), or if you are unable to follow study directions.

If for any reason you want to leave the study early, you must talk to the study doctor. It may be life-threatening to leave the study after you have started to receive the study drugs but before you receive the stem cell transplant because your blood cell counts will be dangerously low.

This is an investigational study. All of the drugs used in this study are FDA-approved and commercially available. Up to 70 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients < 65 years of age with histologically confirmed refractory or relapsed Hodgkin's disease (including patients who fail or relapse after autologous SCT). This upper age limit will apply to transplants from both matched related and unrelated donors.
2. Patients should have any of the following disease status: a. responsive or stable disease on salvage chemotherapy or radiation therapy. b. untreated, smoldering (i.e. not rapidly progressive) relapses.
3. Patients must have a serum bilirubin equal to or </=2.0 mg/dl (isolated hyperbilirubinemia related to Gilbert's disease allowed), serum transaminase (ALT) equal to or </= 3 times the upper limit of the normal range, serum creatinine <2.0 mg/dl (provided they also have a glomerular filtration rate of at least 55 ml/min), no symptomatic cardiac or pulmonary disease and a performance status equal to or </=2. Left ventricular ejection fraction >/= 40%, forced expiratory volume at one second (FEV1), forced vital capacity (FVC) and corrected diffusing capacity of lung for carbon monoxide (DLCO) >/= 50% predicted.
4. Patients must have an HLA-compatible related or unrelated donor (one-antigen mismatched related donors are acceptable) willing to donate marrow or rhG-CSF-mobilized peripheral blood stem cells. In the event of transplants from matched unrelated donors, a high-resolution allele match for HLA-A, -B, -C, -DRB1 ("8 of 8 match") is required.
5. Women of childbearing potential must have a negative serum pregnancy test within two weeks of study entry and should be advised to avoid becoming pregnant. Men should be advised to not father a child while on treatment. Both women of childbearing potential and men must agree to practice effective methods of contraception.
6. Patients must be capable and willing to sign informed consent.

Exclusion Criteria:

1. Patients with documented disease progression on salvage chemotherapy.
2. Nursing or pregnant females. Should a woman become pregnant or suspect she is pregnant while participating in the study, she should inform her treating physician immediately.
3. Severe concomitant medical or psychiatric illness.
4. Uncontrolled arrhythmia or symptomatic cardiac or pulmonary disease.
5. Chronic active hepatitis or cirrhosis.
6. Active or uncontrolled infection.
7. Radiation therapy involving chest (axilla excluded), mediastinum, or abdomen (i.e., small or large bowel) completed within 10 weeks of transplant admission. Radiation therapy shortly before the start of the preparative regimen is allowed.
8. Prior or concurrent malignancies (including myelodysplasia) except resected basal cell carcinoma or treated carcinoma in-situ. Cancer treated with curative intent < 5 years previously will not be allowed unless approved by the Protocol Chair. Cancer treated with curative intent > 5 years previously will be allowed.