Abstract: Chronic myeloid leukemia (CML) is a blood stem cell disorder characterized by overproduction and accumulation of myeloid cells, particularly neutrophils. The disease is driven by a small pool of malignant stem cells, and passes through three phases: an initial chronic phase (CP-CML), an intermediate advanced phase (AP-CML), and a terminal blast phase (BP-CML). Within each myeloid cell, the hallmark of CML is the presence of BCR-ABL, an oncoprotein that constitutively activates numerous cell signaling pathways. Drug discovery efforts targeting BCR-ABL have led to Gleevec, a small molecule inhibitor that competes with ATP for the ATP-binding pocket in the oncoprotein. Gleevec induces durable disease remission during CP-CML, but disease relapse often occurs during AP-CML and in particular BP-CML due to development of Gleevec resistance. In addition, relapse frequently occurs after discontinuation of therapy even after several years of treatment, and observation that raises questions concerning how effectively Gleevec attacks leukemic stem cells. Here, we examine questions related to these two issues by constructing and comparing Gleevec pharmacokinetic and mechanistic subcellular- and cellular-level pharmacodynamic models. At the subcellular level, one model best-fitted to the experimental data hypothesized the existence of an uncharacterized drug clearance mechanism, and we speculated that this specific mechanism might be PGP-mediated efflux from the cell. This hypothesis was subsequently verified experimentally. A second model, also best-fitted to the data, hypothesizes that subcellular sequestration is another resistance mechanism. At the cellular level, the models which best-fit the experimental data set were ones in which Gleevec was postulated to deplete the size of the malignant stem cell pool, although they do not shown eradication taking place. Taken together, these results provide potentially significant insight into how Gleevec affects both the subcellular- and cellular-level dynamics of CML.