The rheology of end-tethered polymer layered silicate nanocomposites is investigated using linear viscoelastic measurements in oscillatory shear with small strain amplitudes. Two systems consisting of poly(epsilon-caprolactone) and nylon-6 with varying amounts of layered silicate (montmorillonite) are examined. The storage (G’) and loss (G ") moduli increase at all frequencies with increasing silicate loading, consistent with previous findings with conventionally filled polymer systems. However, the power-law dependence of G’ and G " in the terminal zone is different from that observed in homopolymers and decreases with increasing silicate loading. At low frequencies the rheological response becomes almost invariant with frequency, suggestive of a solid-like response. Comparisons are drawn with rheology of other intrinsically anisotropic materials, and an attempt is made to explain phenomenologically their rich-theological behavior.