N99-02: Melphalan and Buthionine Sulfoximine

Inclusion Criteria: * Patients have relapsed neuroblastoma and must have exhausted all other options for treatment before they can be considered for treatment on this study. * Relapsed patients who are greater than 6 months since having a stem cell transplant can enter on this study. * Patients must have stem cells collected and stored before starting treatment. * Patients must have a double lumen central venous line in place. * Patients must have adequate kidney and liver function measured by blood tests and test of renal function (creatinine clearance or glomerular filtration rate (GFR)). * Patients must have normal heart and lung function measured by lack of physical evidence or clinical history of difficulties breathing and tests of cardiac function (Echocardiogram or MUGA evaluation). * Patients must have an essentially normal neurological exam. * Patients must have one entire kidney that has not had any radiation at treatment doses. (Xrays and scans are ok). * Patients must have recovered from the effects of any prior treatment for their tumor. Exclusion Criteria: * They have had any radiation therapy to the brain. * They have known history of or current tumor found in the brain or surrounding tissues. * They have a history of seizures. * They have a history of changes in a test of kidney function with antibiotic use in the 6 months immediately before entering on this study.