Inclusion Criteria:

          -  Patients must be > 24 months and < 30 years of age when registered on study.

          -  Patients must have relapsed neuroblastoma, refractory neuroblastoma that had less than
             a partial response to standard treatment or persistent neuroblastoma that had at least
             a partial response to frontline therapy frontline therapy with > 3 residual lesions on
             end-induction MIBG scan.

          -  Patients must have evidence of MIBG uptake into tumor at ≥ one site within 4 weeks
             prior to entry on study and subsequent to any intervening therapy.

          -  Patients must have adequate heart, kidney, liver and bone marrow function. Patients
             who have bone marrow disease must still have adequate bone marrow function to enter
             the study.

          -  Patients must have a dose of unpurged peripheral blood stem cells is 2.0 x 106 viable
             CD34+ cells/kg available.

        Exclusion Criteria:

          -  They have had previous I-131 MIBG therapy

          -  They have other medical problems that could get much worse with this treatment.

          -  They are pregnant or breast feeding.

          -  They have a history of a venous or arterial thrombosis that was not associated to a
             central line.

          -  They have active infections such as hepatitis or fungal infections.

          -  They have active diarhhea.

          -  They have had an allogeneic stem cell transplant (received stem cell from someone
             else)

          -  They can't cooperate with the special precautions that are needed for this trial.