OUTLINE: Patients are stratified according to disease category (primitive neuroectodermal tumor vs Ewing's sarcoma). Patients receive treatment on regimen A as outlined below during courses 1-3 and 6 and regimen B as outlined below during courses 4, 5, and 7 in the absence of disease progression or unacceptable toxicity. Each course lasts 3-4 weeks. Patients without metastatic disease after completion of course 3 undergo complete tumor resection, if feasible. Patients achieving complete response with or without microscopic residual disease after completion of course 7 undergo radiotherapy twice daily, 5 days a week, for 3 weeks. Patients with gross residual disease after completion of course 7 undergo radiotherapy twice daily, 5 days a week, for 3.6 weeks. Regimens A and B are defined below: Regimen A: Patients receive cyclophosphamide IV over 6 hours on days 1 and 2, doxorubicin IV continuously and vincristine IV continuously on days 1-3, and vincristine IV on day 9. Regimen B: Patients receive etoposide IV over 1 hour, followed immediately by ifosfamide IV over 1 hour on days 1-5. Patients are followed monthly for 18 months and then every 6 months for 18 months.