A recently developed unified constitutive model for creep-ageing of an Al-Cu-Li alloy (AA2050-T34) has been successfully extended to applications of multistep heat treatments of aluminium alloys, including natural and artificial ageing with simple and complex hardening evolution and creep-ageing with different initial temper conditions. An age hardening model for both natural and artificial ageing was proposed based on the unified creep-ageing constitutive model and methods to determine the initial and equilibrium values of both micro and macro variables of aluminium alloys under general heat-treated conditions were presented. By unifying normalised microstructural variables throughout the multistep heat treatments, the model was able to predict both the simple and complex strengthening evolution of various aluminium alloys during ageing and creep-ageing. A number of case studies were carried out for natural ageing, artificial ageing and creep-ageing of some typical heat-treatable aluminium alloys, including 2xxx (Al-Cu-Mg and Al-Cu-Li) and 7xxx (Al-Zn-Mg) alloys with as-quenched, naturally-aged (T3/T4) and peak-aged (T6/T8) initial temper conditions. Excellent agreement has been achieved between experimental and simulation results.