A mathematical model of time-dependent cellular damage, repair, killing and repopulation of bone marrow following treatments with ionizing radiations is described. Effects from variable dose rates, multiple exposures, different radiation sources and arbitrary intervals between treatments can be modeled by ordinary differential equations. Of several unique features, the most unusual is that rate constants for injury, repair, killing and proliferation of cells are evaluated by likelihood analysis of animal mortality data. Results indicate that a relatively radioresistant pool of bone marrow cells mediates the proliferation of the hematopoietic stem cells. Applications include modeling of 1) myelopoietic integrity as a function of time and dose rate, 2) the whole-body survival curve (at any point in the treatment protocol) for cells critical to myelopoiesis, 3) a prompt dose equivalence from any completed portion of a therapeutic schedule and 4) potential gain from schedule changes during the course of the treatment.