Although superior high temperature tensile yield strength of high entropy superalloys (HESAs) arises from their hierarchical microstructure, the precipitation processes driving its formation remains unclear. In the present study, we analyze the kinetics of gamma' and gamma precipitations by treating the concurrent nucle-ation, growth and coarsening using common computational thermodynamic and kinetic tools to simulate the microstructure genesis and evolution in HESA during thermal treatments. The ability of the simulations to reproduce the experimentally observed microstructure parameters is evaluated. Temperature time-transformation (TTT) diagrams are calculated to serve as guidelines for further optimization of the hierarchical microstructure of HESAs. (C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.