We investigate the changes in the microstructure on a nano-scale (nano-structure) in technically used AlCuMg 2024 alloys. We show how the annihilation parameters, i.e. the positron lifetimes and corresponding intensities, are changing during natural and artificial aging. It turns out that positron annihilation spectroscopy is very sensitive to changes occurring in the nano-structure but which are not always reflected or measurable in the materials properties such as hardness. The detected changes in the positron lifetime, corresponding to trapping at precipitations, indicate transport of copper atoms through the aluminum matrix to the precipitations. Multi-component spectra for very long aging times indicate that the distances between the trapping centers have increased. This means that the precipitations grow in size, while their number decreases.