In this paper, the precipitation behaviour of (Ni3(Nb,Al)) and ’ (Ni3(Al,Ti,Nb)) phases in the nickel-base superalloy ATI Allvac® 718PlusTM, as well as their kinetic interactions are discussed. Important parameters such as volume fraction, mean radius and number density of precipitates are experimentally determined and numerically simulated as a function of the heat treatment parameters time and temperature. To match the experimentally observed kinetics, the predicted interfacial energy of the precipitates, as calculated for a sharp, planar phase boundary, is adjusted to take into account the interfacial curvature and entropic effects of a diffuse interface. Correction functions for the interfacial energies of as well as ’ precipitates are presented. Using these modified interfacial energies, the calculated results show excellent agreement with the experimental measurements.