  We apply the post-quasi--static approximation, an iterative method for the
evolution of self-gravitating spheres of matter, to study the evolution of
anisotropic non-adiabatic radiating and dissipative distributions in General
Relativity. Dissipation is described by viscosity and free-streaming radiation,
assuming an equation of state to model anisotropy induced by the shear
viscosity. We match the interior solution, in non-comoving coordinates, with
the Vaidya exterior solution. Two simple models are presented, based on the
Schwarzschild and Tolman VI solutions, in the non--adiabatic and adiabatic
limit. In both cases the eventual collapse or expansion of the distribution is
mainly controlled by the anisotropy induced by the viscosity.
