The equilibrium rheological properties of a range of isotropic exfoliated and intercalated hyperbranched polymer (HBP)/montmorillonite (MMT) clay nanocomposites have been investigated using low strain oscillating shear measurements at temperatures above the glass transition temperature of the HBP. Predominantly exfoliated nanocomposites showed a sharp increase in shear viscosity at about 0.8 wt % MMT, associated with a transition from Newtonian to solid-like behavior, which was characterized in terms of a limiting shear modulus at low frequencies and a limiting viscosity at high frequencies, both of which were strongly dependent on the MMT content. Intercalated HBP/organically modified MMT nanocomposites showed qualitatively similar behavior, but the increase in viscosity with MMT content was far weaker. This was argued to reflect a significantly lower effective particle aspect ratio than in the exfoliated nanocomposites.