OUTLINE: This is a two-stage study. Patients will receive cytarabine either by continuous infusion (first stage) or bolus injection (second stage). Patients are stratified by disease (stage III non-Hodgkin's lymphoma (NHL) vs stage IV NHL vs stage B acute lymphoblastic leukemia). Therapy for all patients consists of alternating courses of "A" and "B". Patients with stage III disease receive 4 courses of chemotherapy (ABAB) while those with stage IV disease and B cell acute lymphoblastic leukemia receive 6 chemotherapy courses (ABABAB). Course A - Induction: Patients receive intrathecal methotrexate (IT MTX) and intrathecal cytarabine (IT Ara-C) on days 1, 4, and 11. Dexamethasone is administered by IV or orally twice a day on days 1-5. Cyclophosphamide IV is administered every 12 hours on days 1-3. Doxorubicin IV is administered over 15 minutes beginning 12 hours after the beginning of the 6th dose of cyclophosphamide (day 4). At the same time, vincristine IV is administered, then repeated on day 11. Patients begin filgrastim (granulocyte colony-stimulating factor; G-CSF) subcutaneously or IV over 30 minutes on day 5. Course B - Induction: The first 10 patients enrolled receive cytarabine by continuous infusion while the second 10 patients enrolled receive cytarabine by bolus IV. Patients begin treatment on day 18 and receive methotrexate IV over 24 hours plus IT MTX during hour 1. Dexamethasone is administered by IV or orally twice a day on days 1-5. After completing the 24 hour IV MTX infusion, patients begin cytarabine by continuous infusion over 48 hours or bolus IV every 12 hours for 4 doses. Patients receive G-CSF subcutaneously or IV over 30 minutes beginning on day 22. Patients are assessed for remission status before day 36. Course A - Consolidation: Patients receive dexamethasone IV or orally twice a day on days 1-5. IT MTX and IT Ara-C are administered on days 1 and 4. Cyclophosphamide is administered as during Induction, with vincristine IV and doxorubicin IV over 15 minutes 12 hours later. Vincristine repeats 1 week later. G-CSF administration begins on day 5. Course B - Consolidation: Therapy begins on day 22 with dexamethasone administered as previously. Methotrexate infusion and IT MTX are administered as in Course B - Induction, as is cytarabine (either as a continuous infusion or bolus IV). G-CSF is also administered as previously. Patients are followed monthly for the first 6 months, every 2 months for the next 6 months, then every 6 months for 3 years, then annually thereafter.