The present paper describes the physical and mathematical basis for handling coupled nucleation, growth and coarsening 4 small precipitates during thermal processing of age hardening aluminium alloys. The numerical solution algorithm is based on a finite difference formulation, where the particle size distribution is divided into a series of small radius elements. These elements are treated as one-dimensional control volumes, in which the particles are allowed to enter or leave as their radius changes due to dissolution or growth. Well established dislocation theory is then used to calculate the resulting change in hardness or yield strength at room temperature, based on a consideration of the intrinsic resistance to dislocation motion due to solute atoms and particles, respectively, following heat treatment. Both solution algorithms have been implemented;is separate subroutines in a previously developed FE code for welding, known as WELDSIM. The thermal module of WELDSIM provides the required temperature history for each material point of the solution domain which, ill turn, is used as input to the microstructure model. In the paper, results from simulations and measurements of the microstructure and strength evolution during ageing, welding and post-weld heat treatment of Al-Mg-Si alloys are presented. These show that the transformations have a strong memory of the past process steps due to interactions between different groups or classes of particles that form at various temperatures.