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The goal of this study is to model the creep and recovery response of fine asphalt mixtures using a thermodynamically consistent nonlinear viscoelastic model. The model considers asphalt mixture to consist of two constituents: aggregate structure incorporating the asphalt–aggregate interface and asphalt binder. The efficacy of the model is evaluated using the response of warm fine aggregate mixtures (WFAM). These materials were produced using a polymer-modified binder of PG 76-22 and three warm mix additives (Sasobit, Advera and Rediset). Unaged and aged samples were subjected to creep stress levels of 75 and 400 kPa followed by rest periods. The model was quite successful in capturing the material behaviour as a single set of parameters were derived from the prediction of shear and normal stress responses for both 75 and 400 kPa stress levels. The presented model offers a unique feature in modelling the energy storage and dissipation of each of the two constituents. As such, one can examine the effect of changes in individual material properties on the material response and performance.