Objective of the low-dose transplant regimen must produce the following effects:

1. Suppression of the patient's immune system to prevent rejection of the donor cells;
2. Control of the lymphoma. The pretransplant regimen must suppress the lymphoma sufficiently to prevent marked progression of the tumor and allow time for the GVT effect to occur.

Alemtuzumab is a drug that can specifically attack some types of leukemia and lymphoma cells. In addition, it suppresses the patients' immune system, therefore helps preventing the rejection of donor marrow or stem cells.

Before treatment starts, patients will have a physical exam, including blood tests (between 100 - 120 cc) and urine tests. Women who are able to have children will have a pregnancy test. Bone marrow samples will be taken. Patients will have a chest x-ray, CT scans and EKG, and tests of lung function.

Blood tests (between 100 - 120 cc) marrow sampling, and x-rays will be done as needed to track the effects of the transplant. For bone marrow sampling, a large needle is placed into the numbed hipbone. The bone marrow is then withdrawn through the needle. Patients will have transfusions of blood and platelets as needed. Blood tests (between 100 - 120 cc) will be done daily while patients are in the hospital.

Alemtuzumab will be injected into the patient's vein. This will be done 3 days in a row (days 1 to 3). The drugs diphenhydramine (Benadryl) and acetaminophen (Tylenol) will be given in to prevent or ease side effects.

Patients will also receive fludarabine and cyclophosphamide daily for 3 days. They will be given on the same days as alemtuzumab. Rituximab will be given (to some patients only, based on the subtypes of lymphomas) eight days before the transplant and then weekly for a total of 4 doses.

All of the chemotherapy drugs will be given through a catheter (plastic tube) that extends into the large chest vein. The catheter will be left in place throughout treatment. When chemotherapy is finished, blood stem cells from a donor will be given through the catheter. G-CSF, a growth factor that promotes the production of blood cells, will be injected under the skin once a day until the neutrophil counts recover in the blood.

A "boost" of donor cells (lymphocytes) will be given at 3 months after transplant if the disease is getting worse or if DNA tests from the blood shows that not all lymphocytes in the blood are from the donor. These cells will be given through the vein, without chemotherapy, in the clinic.

Treatment will be given in the hospital at M. D. Anderson. Patients will need to stay in the hospital for about 3 to 4 weeks. Patients will be taken off study if their disease progresses.

Patients must stay in the Houston area for about 100 days after the transplant. After that, patients will need to return to Houston from time to time for blood tests, urine tests, and other exams.

This is an investigational study. The FDA has approved the drugs used in this study. Their use together in this study is investigational. About 100 patients will take part in this study. All will be enrolled at M. D. Anderson.

Inclusion Criteria:

1. Up to 70 years of age (physiological).
2. Any histological subtype of lymphoid malignancies (those with CD20 negative disease will not receive Rituximab).
3. Patients in relapse with a partial remission or stable disease.
4. Patients who failed a prior autologous transplant are also eligible.
5. Patients must have a matched unrelated donor and no human leukocyte antigen (HLA) identical sibling is available. Point scale (PS)<2.
6. Patients are included even if they were previously exposed to Campath or Rituximab.

Exclusion Criteria:

1. Past history of anaphylaxis following exposure to rat- or mouse-derived COR-grafted humanized monoclonal antibodies.
2. Less than 4 weeks since prior chemotherapy counted from 1st day of treatment regimen.
3. Pregnancy or lactation.
4. HIV or HTLV-I positively.
5. Serum creatinine >1.6mg/dl or serum bilirubin >1.5mg/dl unless due to tumor.
6. Pulmonary function tests (PFTs) -OLCO<50%, cardiac EF <50% of predicted levels.
7. Patient with severe concomitant medical or psychiatric illness.