Age hardening of Al-Cu-Mg type alloys occurs in two stages separated by a constant hardness plateau when the alloys are aged at 110°C to 240C after solution treatment and quenching. This work aims to develop a physically based two-stage hardening model to predict the yield strength of Al-Cu-Mg alloys with compositions in the (+S) phase region. Experiments by means of hardness and tensile tests, differential scanning calorimetry and transmission electron microscopy (TEM) have been carried out to provide the relevant information for the calibration and validation of the model. The model considers a simplified precipitation sequence which involves a pre-precipitate structure followed by S phase. This pre-precipitate structure is referred to as Cu-Mg co-clusters instead of GPB zones based on atom probe and TEM studies from collaborators and a review of the literature. The competition between the Cu-Mg co-clusters and the S phase is modelled by assuming S phase forms at the expense of Cu-Mg co-clusters. In the model, the solvi of the Cu-Mg co-clusters and the S phase are calculated, the evolution of precipitates in terms of volume fraction, average size and the solute concentration in the matrix are described and the superposition of various contributions from precipitation strengthening, solution strengthening and dislocation strengthening are modelled. Strengthening by Cu-Mg co-clusters and S phase is described by the modulus strengthening mechanism and the Orowan bypassing mechanism, respectively. The predicted contributions to the critical resolved shear stress show that strengthening in the alloys is mainly due to the Cu-Mg co-clusters in the first stage of hardening and due to the S phase in the second stage of hardening. The model takes account of the composition dependency of precipitation rate for Cu-Mg co-clusters formation as well as the amount of Cu and Mg present in undissolved intermetallic phases. With a training root mean square error of 12MPa on an artificially aged 2024 alloy, the modelling accuracy on unseen yield strength data of two other alloys is 16MPa. Using a single set of parameters, the model has been applied to predict the hardness of a 2024-T351 alloy artificially aged at low temperature followed by short term underageing at higher temperature and then room temperature ageing. Good agreement between the predictions and the experiments indicates that the hardness changes during these multi-stage heat treatments can be well interpreted by considering Cu-Mg co-cluster dissolution, S precipitation and Cu-Mg co-cluster re-formation. Application to Al-xCu-1.7Mg alloys (x=0.2, 0.5, 0.8 and 1.1at.%) has shown good predictive capabilities of the model for the first stage of hardening. It is also shown that the model is applicable to Al-Cu-Mg alloys with Si contents at levels of 0.1-0.2wt.%. Modelling results of various Al-Cu-Mg alloys during natural ageing, artificial ageing and multi-stage heat treatments indicate that the model is capable of predicting the evolution of microstructure and the yield strength as a function of composition and heat treatments, and can provide a predictive tool for predicting the strength of Al-Cu-Mg based welds.