A set of unified constitutive equations is presented that predict the asymmetric tension and compression creep behaviour and recently observed double primary creep of pre-stretched/naturally aged aluminium-cooper-lithium alloy AA2050-T34. The evolution of the primary micro- and macro-variables related to the precipitation hardening and creep deformation of the alloy during creep age forming (CAF) are analysed and modelled. Equations for the yield strength evolution of the alloy, including an initial reversion and subsequent strengthening, are proposed based on a theory of concurrent dissolution, re-nucleation and growth of precipitates during artificial ageing. We present new observations of so-called double primary creep during the CAF process. This phenomenon is then predicted by introducing effects of interacting microstructures, including evolving precipitates, diffusing solutes and dislocations, into the sinh-law creep model. In addition, concepts of threshold creep stress σth and a microstructure-dependant creep variable H, which behave differently under different external stress directions, are proposed and incorporated into the creep model. This enables prediction of the asymmetric tension and compression creep-ageing behaviour of the alloy. Quantitative transmission electron microscopy (TEM) and related small-angle X-ray scattering (SAXS) analysis have been carried out for selected creep-aged samples to assist the development and calibration of the constitutive model. A good agreement has been achieved between the experimental results and the model. The model has the potential to be applied to creep age forming of other heat-treatable aluminium alloys