This is a clinical gene transfer study that aims to verify the safety and efficacy of the use of the EFS-ADA lentiviral vector to introduce the human adenosine deaminase (ADA) gene into the hematopoietic progenitors of patients affected with severe combined immunodeficiency due to ADA deficiency. The EFS-ADA vector expresses the human ADA cDNA under the control of the elongation factor alpha short promoter (EFS). In addition, this protocol will examine the effects of the ADA gene transfer on the immune system of treated patients. Patients with ADA deficiency and ineligible for matched sibling allogeneic bone marrow transplantation are eligible to participate in the study. To increase engraftment and selected advantage or gene-corrected cells, busulfan will be used as a cytoreductive agent. Enzyme replacement (PEG-ADA) will be discontinued 30 days after infusion of gene-corrected cells. CD34+ hematopoietic progenitors will be isolated from the patient bone marrow, peripheral blood or cord blood, exposed to lentiviral vector-mediated gene transfer and re-infused into the patient through a peripheral vein. Clinical, immunological and molecular follow-up studies will assess safety, toxicity, and efficacy of the procedure.