Several studies have demonstrated age-related regional differences in the magnitude of the BOLD signal using task-based fMRI. It has been suggested that functional changes reflect either compensatory or de-differentiation mechanisms, both of which assume response to a specific stimulus. Here, we have tested whether ageing affects both task-based and resting brain function, and the extent to which functional changes are mediated by reductions in grey matter (GM) volume. Two groups, of 22 healthy younger and 22 older volunteers, underwent an imaging protocol involving structural and functional MRI, both during a memory task and at rest. The two groups had similar socio-demographical characteristics and cognitive performance. Image analysis revealed both structural and functional differences. Increased BOLD signal in older relative to younger volunteers was mainly observed in the frontal lobes, both during the task and at rest. Functional changes in the frontal lobes were largely located in brain regions spared from GM loss, and adding GM covariates to the fMRI analysis did not significantly alter the group differences. Our results are consistent with the suggestion that, during normal ageing, the brain responds to neuronal loss by fine-tuning connections between spared neurons. Longitudinal studies will be necessary to fully test this hypothesis.