  Various spatial-gradient extensions of standard viscoelastic rheologies of
the Kelvin-Voigt, Maxwell's, and Jeffreys' types are analyzed in linear
one-dimensional situations as far as the propagation of waves and their
dispersion and attenuation. These gradient extensions are then presented in the
large-strain nonlinear variants where they are sometimes used rather for purely
analytical reasons either in the Lagrangian or the Eulerian formulations
without realizing this wave-propagation context.The interconnection between
these two modeling aspects is thus revealed in particular selected cases.
