Treatment of SCID Due to ADA Deficiency With Autologous Transplantation of Cord Blood or Hematopoietic CD 34+ Cells After Addition of a Normal Human ADA cDNA by the EFS-ADA Lentiviral Vector

* INCLUSION CRITERIA: Participants must satisfy Inclusion Criteria I, II, and III. I. Children greater than or equal to 1.0 month of age with a diagnosis of ADA-deficient SCID based on: A. Confirmed absence (\<3% of normal levels) of ADA enzymatic activity in peripheral blood or (for neonates) umbilical cord erythrocytes and/or leukocytes, skin fibroblasts or in cultured fetal cells derived from either chorionic villus biopsy or amniocentesis, prior to institution of enzyme replacement therapy. AND B. Evidence of severe combined immunodeficiency based on either: 1. Family history of first order relative with ADA deficiency and clinical and laboratory evidence of severe immunologic deficiency, OR 2. Evidence of severe immunologic deficiency in subject prior to institution of immune restorative therapy, based on lymphopenia (absolute lymphocyte count \<200/microliters) or severely decreased T lymphocyte blastogenic responses to phytohemagglutinin (DeltaCPM\<5,000), II. Ineligible for matched sibling allogeneic bone marrow transplantation due to absence of a medically eligible HLA-identical sibling with normal immune function who may serve as an allogeneic bone marrow donor. III. Signed written informed consent according to guidelines of the UCLA Office of Human Research Protection Program and National Human Genome Research Institute (NHGRI) Institutional Review Boards. It is a policy of the NIH Clinical Center not to admit patients younger than 1 year of age and weighing less than 10 kg because of the inadequacy of the existing emergency and intensive care services for very young children. We will comply with such policy. EXCLUSION CRITERIA (OBSERVED WITHIN 8 WEEKS OF ENTERING THIS TRIAL): 1. Age less than or equal to 1.0 months 2. Hematologic 1. Anemia (hemoglobin \< 10.5 g/dl at \< 2 years of age, or \< 11.5 g/dl at \> 2 years of age). 2. Neutropenia (absolute granulocyte count \<500/mm(3). If ANC\< 1,000, absence of myelodysplastic syndrome on bone marrow aspirate and biopsy and normal marrow cytogenetics. 3. Thrombocytopenia (platelet count \< 150,000/mm(3), at any age). 4. PT or PTT \> 2 times the upper limits of normal (patients with a correctable deficiency controlled on medication will not be excluded). 5. Cytogenetic abnormalities on peripheral blood or bone marrow or amniotic fluid (if available). 3. Infectious a. Evidence of active opportunistic infection or infection with HIV-1, hepatitis B, CMV or parvovirus B 19 by DNA PCR within 30-90 days prior to bone marrow harvest. 4. Pulmonary 1. Resting O2 saturation by pulse oximetry \< 95% on room air. 2. Chest x-ray indicating active or progressive pulmonary disease. 5. Cardiac 1. Abnormal electrocardiogram (EKG) indicating cardiac pathology. 2. Uncorrected congenital cardiac malformation with clinical symptomatology. 3. Active cardiac disease, including clinical evidence of congestive heart failure, cyanosis, hypotension. 4. Poor cardiac function as evidenced by LV ejection fraction \< 40% on echocardiogram. 6. Neurologic 1. Significant neurologic abnormality by examination. 2. Uncontrolled seizure disorder. 7. Renal 1. Renal insufficiency: serum creatinine greater than or equal to 1.2 mg/dl, or greater than or equal to 3+ proteinuria. 2. Abnormal serum sodium, potassium, calcium, magnesium, phosphate at grade III or IV by Division of AIDS Toxicity Scale. 8. Hepatic/GI: 1. Serum transaminases \> 5 times the upper limit of normal (ULN). 2. Serum bilirubin \> 2 times ULN. 3. Serum glucose \> 1.5 times ULN. 4. Intractable severe diarrhea. 9. Oncologic 1. Evidence of active malignant disease other than dermatofibrosarcoma protuberans (DFSP)\* 2. Evidence of DFSP expected to require anti-neoplastic therapy within the 5 years following the infusion of genetically corrected cells 3. Evidence of DFSP expected to be life limiting within the 5 years following the infusion of genetically corrected cells 10. Known sensitivity to Busulfan 11. General 1. Expected survival \< 6 months. 2. Pregnant. 3. Major congenital anomaly. 4. Ineligible for autologous HSCT by the criteria at the clinical site. 5. Other conditions which in the opinion of the principal investigator and/or co-investigators, contra-indicate the bone marrow harvest, the administration of busulfan, infusion of transduced cells or indicate the patient or patient s parents/primary caregivers inability to follow protocol. * DFSP is a rare, locally invasive tumor with low metastatic potential. Patients receiving active anti-neoplastic therapy for any cancer, including DFSP, are not eligible. Patients with DFSP who are not being treated with active anti-neoplastic therapy at the time of enrollment AND have no plan to receive active anti-neoplastic therapy in the absence of progressive malignant disease AND whose DFSP is not expected to be life-limiting within the five years following the infusion of genetically corrected cells are eligible. Patients with DFSP, for whom radiation or chemotherapy has been chosen, would remain ineligible during treatment, as the interaction of busulfan and the experimental gene transfer vectors with active anti-neoplastic therapy is difficult to predict and could reasonably be expected to be deleterious due to overlapping toxicities. When anti-neoplastic therapy is concluded, patients with ADA-SCID and a history of DFSP can be included.