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The two drugs, Paclitaxel and Cisplatin, have important roles in the treatment of breast and ovarian cancer, with the combination currently considered the optimum first line chemotherapy of epithelial ovarian cancer. There has been a variety of experimental and clinical studies to try to determine the most effective method to deliver these drugs. These studies consistently show that giving Paclitaxel prior to Cisplatin is the more effective regimen. However, the reasons why are not fully understood. Therefore, we have developed a mathematical model to describe and predict the effects of these two drugs. This model takes into account the cytotoxic effects of the drugs on the cell-cycle and the pharmacodynamic and pharmacokinetic effects of the drugs on each other. The model agrees with the experimental and clinical studies which show that Paclitaxel given prior to Cisplatin is the better combination and, in addition, the model also predicts more effective treatment regimens. These include conditions on the time between doses and the dosing of each of the drugs.