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Microstructural changes during heat treatment of the Ni-based CMSX-4 and CMSX-6 superalloys have been investigated experimentally and simulated using a phase-field multi-component model incorporating elastic driving forces in the presence of a lattice misfit. Furthermore, a theoretical model of the coarsening of anisotropic particles is proposed for the prediction of the main kinetic parameters of the coarsening process. A comparison of the main characteristics of the microstructural evolution during non-directional γ′-coarsening, provided from both experiments and phase-field simulations, gives a good agreement of the coarsening kinetics of the CMSX-4 superalloy. However, for the CMSX-6 superalloy, phase-field simulation results and theoretical predictions are not entirely consistent with experimental results, and show that additional effects, for example, those caused by plastic deformation, might be a reason for the slow coarsening rate.