  We present the first systematic measurements of the dynamic response of a
glassy soft-solid formed on dispersing colloids in a thermotropic nematic
liquid crystal. Through applying a simple theoretical model, we reveal that the
nematic elasticity dominates at low frequencies (longest timescales) and
prevents flow. The Ericksen number $E_R$, determines a critical frequency
$\omega_c$, above which the viscous component $G'' \propto \omega ^{1/2}$. We
find that the value of tan$\delta$ is independent of the colloidal volume
fraction ($\phi$), and is determined by the ratio of lengthscales associated
with the defect-line density and the size of colloid-free nematic regions
trapped within the composite.
