Recently we proposed a constitutive model for structure and total stress in particulate suspensions, in which structural information is represented by a structure tensor that is determined from evolution equations derived from principles of continuum mechanics [Stickel et al., J. Rheol. 50, 379-413 (2006)]. The model was tested by comparing its predictions for structure and stress with results obtained from Stokesian dynamics simulations of hard-sphere suspensions in steady shear flow. Here we apply the same model to time-dependent shear flows. We compare our results with Stokesian dynamics simulations for flows with step discontinuities in the shear rate, including startup, step increases and decreases in shear rate, and flow reversal. In addition, comparisons are made with experimental results from the literature, both for shear flows with step discontinuities and sinusoidally varying shear rates. It is shown that the model predictions are in good quantitative agreement with the simulation results. The predictions also show good qualitative agreement with the experimental data. Some experimental observations, such as the plateau in the dynamic viscosity in the limit of low and high strain amplitudes, are reproduced well. In that case, the model also provides structural information that elucidates the underlying cause for the experimental observations. However, immediately after a flow reversal, the model does not capture the incomplete stress recovery, or irreversibility, that is observed experimentally. (c) 2007 The Society of Rheology.