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In the United States, the Acute Leukemia Task Force has been studying ways to achieve chemical control over the acute leukemias. It was found that L1210 mouse leukemia is an excellent predictive model for childhood acute leukemia. Examination of the kinetics of cell generation led to the conclusions that a single cell could multiply to a lethal number of cells in a relatively short time, and that therapy must destroy every cell. Extension of these hypotheses to childhood leukemia has permitted estimates of generation time of human leukemic cells; the size of the leukemic cell population at clinical relapse and the fractional destruction of cells by individual drugs. By the use of combinations of antileukemic drugs complete cell destruction has been approached in a few patients with early leukemia.