For tuberculosis and number of other bacterial infections, treatment with a single antimicrobial drug frequently fails due to the ascent of mutants resistant to that drug. To minimize the likelihood of this occurrence, multiple drugs with independent resistance mechanisms are used simultaneously. None the less, multiply resistant bacteria sometimes emerge even when patients are simultaneously treated with two or more drugs, and the ascent of these multiply-resistant mutants may result in treatment failure in the patient and spread of these resistant bacteria to other hosts. We consider two mathematical models of antibacterial chemotherapy which can account for the ascent of multiple antibiotic resistance within hosts treated with multiple antibiotics. In both, multiple resistance evolves because of selection favouring mutants resistant to fewer than all of the chemotherapeutic agents employed, intermediates. In one model, this occurs because of temporal fluctuations in the concentrations of the antibiotics in the course of normal treatment and/or because of non-adherence to the treatment regime. In the other, intermediates are favoured and multiple resistance evolves because of tissue and somatic cell heterogeneity. In the effective concentrations of the antibiotics and physiological variation in the sensitivity of subpopulations of bacteria to different antibiotics. We discuss the limitations (and assets) of this model and approach and the implications for the design of antibiotic treatment regimes. Finally, we consider how the assumptions behind this model and the predictions made from its analysis could be tested experimentally.