The melt-state linear and nonlinear shear rheological properties of hybrid materials of polypropylene and amine-exchanged montmorillonite were studied. The materials were prepared by melt mixing with maleic anhydride functionalized polypropylene as the compatibilizer. The clay interlayer spacing las determined by wide-angle X-ray scattering) increased upon melt mixing; however, the short-range ordering of the clay layers was preserved. Above inorganic loadings of 2.0 wt % the hybrid materials exhibited apparent low-frequency plateaus in the linear viscoelastic moduli. The hybrid storage modulus was sensitive to the chemistry of the amine exchanged into the clay. The amount of stress overshoot observed in flow reversal experiments was found to be a function of the rest time allowed between the reversal. The transient stress in start-up of steady shear scaled with the applied strain. These observations allow features of the polypropylene/montmorillonite hybrid structure to be deduced. The transient nonlinear rheology is consistent with an anisometric, non-Brownian structure. These anisometric particulate domains are mesoscopic, and internally, they contain multiple, ordered platelets. This mesoscopic structure is itself thermodynamically unstable, because the rheology indicates that quiescent structural evolution whose origin is not Brownian relaxation is observed. The demonstration of the sensitivity of melt-state rheological measurements to interparticle structure and chemistry of the hybrid materials indicates the potential usefulness of such studies for the development of new nanocomposite materials.