Mitochondrial DNA (mtDNA) mutations accumulate in the skeletal muscle of patients with mtDNA disease, and also as part of healthy ageing. Simulations of human muscle fibres suggest that, over many decades, the continuous destruction and copying of mtDNA (relaxed replication) can lead to dramatic changes in the percentage level of mutant mtDNA in non-dividing cells through random genetic drift. This process should apply to both pathogenic and neutral mutations. To test this hypothesis we sequenced the entire mitochondrial genome for 20 muscle fibres from a healthy elderly 85-year-old individual, chosen because of the low frequency of cytochrome c oxidase negative fibres. Phenotypically neutral single base substitutions were detected in 15% of the healthy fibres, supporting the hypothesis that positive selection is not essential for the clonal expansion of mtDNA point mutations during human life. Treatments that enhance mtDNA replication, such as vigorous excercise, could amplify this process, with potentially detrimental long-term consequences.