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The coarsening kinetics of γ′-precipitates in single crystalline Ni-based superalloys is studied using phase-field simulations. At first, we discuss interdiffusion-limited γ′-coarsening in technologically relevant superalloys with the explicit inclusion of up to nine chemical components. The simulations show that an additional influence from the coherency strain leads to a substantially faster coarsening-evolution compared to the predictions from the LSW-theory. Second, we perform a virtual experiment to determine the influence of varying rhenium (Re) and ruthenium (Ru) additions on the temporal evolution of the γ-γ′ microstructure under thermo-mechanical loads. We observe that a change in the Re content strongly alters the coarsening kinetics. On the contrary, it is found that Ru variations have no significant effect on the coarsening kinetics.