The purpose of this study is to determine if we can prevent Epstein Barr Virus lymphomas by the monthly administration of an (antibody) protein against B lymphocytes called Rituximab. Although this medicine has been approved by the Food and Drug Administration to treat patients with other types of lymphomas, and has been used to treat a small number of patients with EBV lymphomas and other types of B-cell leukemias, it has not been approved to try and prevent EBV-lymphomas. Use of Rituximab to try to prevent EBV-lymphomas is therefore experimental.

Inclusion Criteria:

• Patient must be a recipient of aT cell depleted unrelated or HLA mis-matched related HSCT for the treatment of a malignancy or immunodeficiency disease.
• Patients must have an ANC > or = to 1500 cells/ul on the day of first treatment.
• Patients with acute or chronic leukemia, or MDS prior to transplant must be in remission defined as <5% blasts in the bone marrow.
• Patient with must be in remission.
• Patient must be Hepatitis B surface antigen negative pre transplant.
• Patients must have adequate cardiac function defined as a left ventricular ejection fraction at rest of >50% documented pre-transplant.
• Patient may be of either gender and of any ethnic background.
• Patient may be of any age. There is no upper age restriction.
• Patients or their guardians must be able to understand the nature and risk of the proposed study and be able to sign consent.

Exclusion Criteria:

• Karnofsky score <70%
• Female patients who are pregnant or lactating.
• Evidence of EBV-LPD or circulating EBV copy number >1000.
• Active uncontrolled bacterial or fungal infection.
• Prior history of Hepatitis B infection or Hepatitis B surface antigen positivity pre transplant.
• HIV-1,2 sero-positive patients.
• Patients or guardians not signing informed consent.
• Patients with prior allergic reaction to Rituximab or other murine monoclonal antibody.
• Patients taking other investigational agents under another protocol unless discussed and approved in advance by Genentech and the IDEC Therapeutic Director.