The melt-state viscoelastic properties of nanocomposites prepared with a symmetrical polystyrene-polyisoprene block copolymer and organically modified layered silicates are examined. Nanocomposites based on three thermodynamically equivalent organically modified layered silicates, primarily differing in lateral disk diameter (d), are studied with small-amplitude oscillatory shear. The effects of the domain structure of the ordered block copolymer and the mesoscale dispersion of the layered silicates on the rheological properties are examined via a comparison of data for the nanocomposites in the ordered and disordered states of the block copolymer. Hybrids prepared with 5 wt % organically modified fluorohectorite (d similar to 10 mum) and montmorillonite (d similar to 1 mum) demonstrate a notable decrease in the frequency dependence of the moduli at low frequencies and a significant enhancement in the complex viscosity at low frequencies in the disordered state. This behavior is understood in terms of the development of a percolated layered-silicate network structure. However, the viscoelastic properties in the disordered state with 5 wt % organically modified laponite (d similar to 30 nm) and in the ordered state of the block copolymer for all layered silicates demonstrate only minor changes from those observed for the unfilled polymer.