Post‐irradiation annealing experiments are often used to obtain clearer information on the nature of defects produced by irradiation. However, their interpretation is not always straightforward without the support of physical models. We apply here a physically‐based set of parameters for object kinetic Monte Carlo (OKMC) simulations of the nanostructural evolution of FeMnNi alloys under irradiation to the simulation of their post‐irradiation isochronal annealing, from 290 to 600 °C. The model adopts a “grey alloy” scheme, i.e. the solute atoms are not introduced explicitly, only their effect on the properties of point‐defect clusters is. Namely, it is assumed that both vacancy and SIA clusters are significantly slowed down by the solutes. The slowing down increases with size until the clusters become immobile. Specifically, the slowing down of SIA clusters by Mn and Ni can be justified in terms of the interaction between these atoms and crowdions in Fe. The results of the model compare quantitatively well with post‐irradiation isochronal annealing experimental data, providing clear insight into the mechanisms that determine the disappearance or re‐arrangement of defects as functions of annealing time and temperature. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)