A new mechanism is proposed for the apparent breakthrough of HIV that occurs approximately 6 months after the commencement of therapy with zidovudine (AZT). Using a simple mathematical model of the interacting population dynamics of HIV and its major host cell in the circulation (the CD4+ lymphocyte), predicted patterns of HIV plasma viraemia in the weeks following treatment with zidovudine are generated. These are in close agreement with observed patterns despite the fact that the model contains no mechanisms for the development of drug-resistant strains of virus. It is suggested that the patterns of viral abundance observed during the first 6 months after treatment may be the result of non-linearities in the interactions between HIV and CD4+ cells, and that it is only after the first post-treatment burst of viral production that drug resistance plays an important role.