A novel set of unified constitutive equations has been developed and validated to describe stress relaxation ageing (SRA) behaviour. The model, based on dynamic ageing and power-law creep relations, can predict the stress relaxation, age hardening response and their interactions at different temperatures, through considering the microstructure evolutions (precipitate radius, volume fraction and dislocation density) during SRA. In addition, the model newly incorporates the effects of prior cold work. This model was verified through T74 multi-step SRA experiments for different pre-strain conditions. Excellent agreement was achieved between the predicted and experimental stress relaxation and yield strength evolutions. The evolutions of microinternal variables (e.g. normalised precipitate radius) within the model were calibrated by both the TEM results in this work and the experimental results from the literature. The model provides a valuable tool to predict the mechanical properties, and residual stresses post ageing, thus provides important guidance for designing manufacturing processes, leading to many benefits including reduced scrap rates and financial losses.