Aim and Scope: The present study is about developing the mathematical model of leukosis according to modern data on hematopoiesis among mammals. Materials and Methods: Three types of cells are considered in the model, one of which is represented by leukemic ones. The interaction of cells is considered as the competition for the functional space of dividing cells. For leukemia cells are the cells dividing at a higher speed as compared to all the others. Results and Discussion: The model of leukemic cells replacement with donor cells is considered as the introduction of more active cells than leukemic ones. The model is represented by the Cauchy problem for the system of ordinary differential equations. Conclusion: The violation of hematopoiesis functions is compared with a leading parameter change, which transfers the system from a stable steady state to an unstable one.