Heteroplasmic mtDNA defects are an important cause of human disease with clinical features that primarily involve nondividing (postmitotic) tissues. Within single cells the percentage level of mutated mtDNA must exceed a critical threshold level before the genetic defect is expressed. Although the level of mutated mtDNA may alter over time, the mechanism behind the change is not understood. It currently is not possible to directly measure the level of mutant mtDNA within living cells. We therefore developed a mathematical model of human mtDNA replication, based on a solid foundation of experimentally derived parameters, and studied the dynamics of intracellular heteroplasmy in postmitotic cells. Our simulations show that the level of intracellular heteroplasmy can vary greatly over a short period of time and that a high copy number of mtDNA molecules delays the time to fixation of an allele. We made the assumption that the optimal state for a cell is to contain 100% wild-type molecules. For cells that contain pathogenic mutations, the nonselective proliferation of mutant and wild-type mtDNA molecules further delays the fixation of both alleles, but this leads to a rapid increase in the mean percentage level of mutant mtDNA within a tissue. On its own, this mechanism will lead to the appearance of a critical threshold level of mutant mtDNA that must be exceeded before a cell expresses a biochemical defect. The hypothesis that we present is in accordance with the available data and may explain the late presentation and insidious progression of mtDNA diseases.