The main purpose of this study is to determine the short and long term side effects of a very intensive treatment, which includes combinations of chemotherapy drugs followed by radiation therapy and two transplants supported by peripheral blood progenitor cells (stem cells), for children with advanced stage neuroblastoma and sarcomas.

• The treatment is separated into three stages: 1) Initial treatment-chemotherapy and stem cell collection; 2) Treatment targeted directly to the main tumor-surgery and radiation therapy; 3) Intensified treatment: two stem cell transplants.
• Patients will receive intensive treatment with a combination of seven drugs which will be given every 3 weeks, or as soon as the patient's blood counts are within safe limits. A total of 5 or 6 courses of chemotherapy will be given. The third and fourth course will be followed by stem cell collections and the last course will be followed by bone marrow harvest in preparation for transplant.
• The first treatment involves a high-dose of Cisplatin intravenously once a day for 5 days and VP-16 intravenously on days 2,3 and 4 of the treatment.
• The second course of treatment involves cyclophosphamide intravenously on day 1 and day 2, adriamycin intravenously continuously over 48 hours, and vincristine intravenously on day 1.
• The third course of treatment involves ifosfamide daily on days 1-5 and VP-16 on days 1-3. Mesna will also be given to prevent bladder irritation.
• During the fourth course patients will receive, carboplatin intravenously on days 1 and 2 and VP-16 on days 1,2 and 3 of treatment.
• The fifth course of treatment will be identical to the second course.
• G-CSF (granulocyte colony-stimulating factor) stimulates bone marrow to produce more white blood cells and will be given subcutaneously until the patients' white blood cell counts are at an acceptable level. This may require 10-14 days of G-CSF treatment.
• After the first two treatments, and after the last course of treatment, patients will be evaluated for response. If significant tumor is still present in the bone marrow before the third treatment, stem cell collection will be delayed. If the bone marrow still shows disease after the next treatment, this plan of treatment will be stopped.
• Patients may undergo surgery after the last treatment to remove the tumor and to evaluate the remaining disease. After recovery, radiation therapy may be performed to the main tumor area.
• Patients will receive transplantations of stem cells twice during this study. After each preparative treatment, half of the patient's stored stem cells will be given intravenously. Until the stem cells restore safe levels of blood cells, the patient will be hospitalized (3-4 weeks or longer).
• The first treatment will begin with high doses of carboplatin and VP-16 daily for 3 consecutive days followed by cyclophosphamide on the fourth and fifth days.
• Between 4-6 weeks after the start of the first course of high dose chemotherapy a second course consisting of melphalan and total body irradiation (TBI) will be given. Melphalan will be given daily for 3 consecutive days followed by TBI twice a day for 3 days.
• After each of the two high dose treatments outlined above, the stem cells that were previously harvested from the patient will be given back to them through a central line.
• Stem cells will be collected on 3 separate occasions following each of two cycles of chemotherapy. They will then be processed using a technique that attempts to separate stem cells from other cells, including any cancer cells that may be present.
• Bone marrow will also be harvested prior to the first transplant and will be used if blood counts do not recover after the stem cells are given.

Inclusion Criteria:

• Previously untreated neuroblastoma Stage D > 365 days
• Previously untreated neuroblastoma Stage C at age > 365 days with n-myc amplification
• Previously untreated metastatic Ewings sarcoma/PNET
• Previously untreated non-rhabdomyosarcoma soft tissue sarcoma
• Confirmation of neuroblastoma at time of diagnosis by histologic specimen or with bone marrow specimen showing solid tumor. Confirmation of sarcoma by histologic specimen with evidence of metastatic disease be imaging study
• Patient 19 years of age or younger
• ANC > 1000
• Platelet count > 75,000
• SGOT < 2.5 x ULN
• Normal serum creatinine levels for age

Exclusion Criteria:

• Previous malignancy requiring nonsurgical treatment or bone marrow transplant.
• Relapsed disease