  One of the main theoretical issues in developing a theory of anisotropic
viscoelastic media at finite strains lies in the proper definition of the
material symmetry group and its evolution with time. In this paper the matter
is discussed thoroughly and addressed by introducing a novel anisotropic
remodelling equation compatible with the principle of structural frame
indifference, a requirement that every inelastic theory based on the
multiplicative decomposition of the deformation gradient must obey to. The
evolution laws of the dissipative process are %obtained by introducing a novel
(remodelling) balance equation which is completely determined by two scalar
functions, the elastic strain energy and the dissipation densities. The proper
choice of the dissipation function allows us to reduce the proposed model to
the Ericksen anisotropic fluid, when deformation is sufficiently slow, or to
the anisotropic hyperelastic solid for fast deformations. Finally, a few
prototype examples are discussed to highlight the role of the relaxation times
in the constitutive response.
