OUTLINE: This is a randomized, multicenter study. Patients are randomized to one of two treatment arms, except for those with CNS disease. These patients are assigned to arm II and receive whole brain irradiation on Regimen B. Arm I: Induction (Modified APO): Patients receive vincristine IV on days 1, 8, 15, 22, and 29, doxorubicin IV over 15 minutes on days 1 and 22, prednisone three times a day on days 1-28, and methotrexate intrathecally (IT) on days 1, 8, and 22. Patients in complete remission on day 43 proceed to maintenance, those in partial remission undergo biopsy then proceed to maintenance, and those with residual disease receive radiotherapy on regimen A concurrently with maintenance. Maintenance (day 1 is day 43 of Induction): Courses of intermediate dose methotrexate/leucovorin calcium and high dose cytarabine (ID MTX/CF/HD ARA-C) and modified APO alternate every 3 weeks. Patients receive a total of 15 courses (8 of ID MTX/CF/HD ARA-C and 7 of Modified APO). ID MTX/CF/HD ARA-C: Patients receive methotrexate IV over 24 hours on day 1, leucovorin calcium IV or orally every 6 hours on days 2 and 3, cytarabine IV over 48 hours on days 2 to 4, and methotrexate IT on day 1 of courses 1, 3, and 5. Filgrastim (G-CSF) is administered beginning on day 5 and continuing until blood counts recover. Modified APO: Patients receive vincristine IV on day 1, oral mercaptopurine on days 1-5, doxorubicin IV over 15 minutes on day 1, and oral prednisone three times a day on days 1-5. Arm II: Induction: Patients receive treatment as in arm I except that patients with CNS disease also receive methotrexate IT on days 15, 29, and 36. Maintenance (day 1 is day 43 of Induction): Modified APO: as in Arm I, with methotrexate administered on day 1 of courses 1, 3, and 5 (days 1-5 for patients with CNS disease). Courses repeat every 21 days for a total of 15 courses. Patients with CNS disease begin radiotherapy on Regimen B on week 2 of maintenance. Regimen A: Patients begin radiotherapy (5 days a week for 4.5 weeks) to residual tumor on day 1 of maintenance. Regimen B: Patients receive whole brain irradiation (5 days a week for 3.1 weeks) beginning on day 1 of maintenance. Patients are followed monthly for 6 months, every 3 months for 18 months, every 6 months for 3 years, and annually thereafter.