Patients who develop EBV viremia or EBV related lymphoproliferative disease after transplant receive autologous Epstein Barr virus (EBV) reactive lymphocytes IV over 20 minutes. Patients receive allogeneic EBV reactive lymphocytes if autologous lymphocytes fail to control EBV proliferation or when sufficient autologous reactive lymphocytes cannot be isolated. Treatment repeats every 4 weeks in the presence of EBV viremia or lymphoproliferative disease. After 5 patients have received therapy without unacceptable toxicity, patients may receive lymphocytes as prophylactic therapy.