Statistical alloy theory based on the Master Equation approach with ab initio calculated interatomic interactions is employed to investigate the growth of precipitates at the early stages of solid solution decomposition, as well as the dissolution of small precipitates during the coarsening stage, upon simulated annealing of ternary Al–Sc–Zr alloys. We show, in agreement with previous studies, that the Zr alloying to Al–Sc alloys promotes the formation of core–shell nanoparticles whose structure is found to be very sensitive to the parameters characterizing the solute diffusion rates in the alloy. We demonstrate that the core–shell structure of precipitates slows down the dissolution of small particles, thus hampering the microstructure coarsening at elevated temperatures.