We study the transient response to simple shear of aqueous dispersions of Laponite clay particles and poly(ethylene oxide) at concentrations for which shear induces structure in the form of a network of polymer–clay bonds. We examine the effects of shear on the structure at the micrometer length scale. Bulk rheometric measurements give the material's response to step changes in shear rate. We find that a critical value of the shear rate separates two regions with different rheological behaviors. Static small-angle light scattering shows a corresponding qualitative change in the anisotropy of the dispersion under shear at the micron scale. We interpret our results in terms of the effects of shear on the interactions between clay particles and polymer chains and on the aggregation mechanisms in the dispersion.