  We develop a continuum theory of linear viscoelastic response in oriented
monodomain nematic elastomers. The expression for dissipation function is
analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we
propose the relations between the anisotropic rubber moduli and new viscous
coefficients. A new dimensionless number is introduced, which describes the
relative magnitude of viscous and rubber-elastic torques. In an elastic medium
with an independently mobile internal degree of freedom, the nematic director
with its own relaxation dynamics, the model shows a dramatic decrease in the
dynamic modulus in certain deformation geometries. The degree to which the
storage modulus does not altogether drop to zero is shown to be both dependent
on frequency and to be proportional to the semi-softness, the non-ideality of a
nematic network. We consider the most interesting geometry for the
implementation of the theory, calculating the dynamic response to an imposed
simple shear and making predictions for effective moduli and (exceptionally
high) loss factors.
