OUTLINE: This is an open label study. Patients are stratified according to age and type of leukemia: Stratum I: Under 20 years old with acute lymphoblastic leukemia (ALL) in second or greater relapse Stratum II: Greater than 20 years old with ALL in first or greater relapse Stratum III: Patients of any age with acute myelogenous leukemia (AML) in first or greater relapse Patients receive aminopterin every 12 hours for 2 doses weekly for 4 weeks. Aminopterin is administered intravenously over 20 minutes for the first, second, and fourth doses, and orally for the third dose. The fifth and all subsequent doses are administered orally if bioavailability is acceptable. Patients receive oral leucovorin calcium every 12 hours for 2 doses beginning 24 hours after the last dose of aminopterin each week. If toxicity is limited for 2 consecutive weeks, the dose of leucovorin calcium is decreased to 1 dose administered 24 hours after the last dose of aminopterin each week. If this schedule is tolerated for 2 consecutive weeks, then leucovorin calcium is discontinued. Patients continue therapy for up to 15 months in the absence of disease progression or unacceptable toxicity. Patients are followed every 6 months.