Leukemia progresses through certain phases starting with slow progressing phases, following in the stability, than transition to acute phase, where there is no more control on the disease. The types of leukemia are grouped by how quickly the disease develops and gets worse. Leukemia is either chronic (gets worse slowly) or acute (gets worse quickly). Treatment depends on a number of factors, including the type of leukemia, the patientís age, whether leukemia cells are present in the cerebrospinal fluid, and whether the leukemia has been treated before. It also may depend on certain features of the leukemia cells. Depending on the type and extent of the disease, patients may have chemotherapy, biological therapy, radiation therapy, or bone marrow transplantation. The objective of the current research is to address the dynamics of Leukemiaís development with the attempts to understand how does the body respond to different type of treatment.