Chronic myeloid leukaemia (CML) is an unusual malignancy in which myeloid progenitor cells are transformed by a single chromosomal translocation where the Bcr domain of chromosome 22 is placed adjacent to the proto-oncogene c-Abl of chromosome 9, resulting in constitutive Abl tyrosine kinase activity. This has a twofold effect: it causes increased numbers of myeloid progenitor cells and circulating myeloid cells, and it causes leakage of reactive oxygen species from mitochondria. We describe a kinetic and pharmacodynamic (PD) model of Bcr-Abl signalling in myeloid cells that is used to simulate effects of four classes of drugs: Bcr-Abl signalling inhibitors, such as imatinib, cyclin-dependent kinase inhibitors, and pro- and anti-oxidants. The model also has the potential to describe the PD effects of agents acting on other sites in the Bcr-Abl signalling pathway. Having calibrated the model against dose-response curves of these drugs acting as single agents on Bcr-Abl-transformed cells in vitro, the model was used to predict effects of the agents in combination. Used in conjunction with pharmacokinetic models, our PD model enables an approach to protocol optimization: large numbers of doses and timings and (in the case of combination treatments) relative dose ratios can be simulated in silico. Predicted selectivity, as well as efficacy, can be extracted from the model. An understanding of the Bcr-Abl signalling pathway has implications for strategies to prevent acquired drug resistance, and for preventing or delaying CML progression to its blast phase.