The cancer stem cell hypothesis has evolved to one of the most important paradigms in
biomedical research. During recent years evidence has been accumulating for the existence
of stem cell-like populations in different cancers, especially in leukemias. In the
current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We
apply the model to compare cellular properties of leukemic stem cells to those of their
benign counterparts. Using linear stability analysis we derive conditions necessary and
sufficient for expansion of malignant cell clones, based on fundamental cellular
properties. This approach reveals different scenarios of cancer initiation and provides
qualitative hints to possible treatment strategies.