We use the Millennium Simulation series to study how the dynamical state of dark matter haloes affects the relation between mass and concentration. We find that a large fraction of massive systems are identified when they are substantially out of equilibrium and in a particular phase of their dynamical evolution: the more massive the halo, the more likely it is found at a transient stage of high concentration. This state reflects the recent assembly of massive haloes and corresponds to the first pericentric passage of recently accreted material when, before virialization, the kinetic and potential energies reach maximum and minimum values, respectively. This result explains the puzzling upturn in the mass–concentration relation reported in recent work for massive haloes; indeed, the upturn disappears when only dynamically relaxed systems are considered in the analysis. Our results warn against applying simple equilibrium models to describe the structure of rare, massive galaxy clusters and urge caution when extrapolating scaling laws calibrated on lower mass systems, where such deviations from equilibrium are less common. The evolving dynamical state of galaxy clusters ought to be carefully taken into account if cluster studies are to provide precise cosmological constraints.