The Herrera-Jiménez-Ruggeri method is employed to analyse the evolution of anisotropic radiating fluid spheres endowed with viscous stresses. The growth of the anisotropy with the distance to the centre allows us to divide the sphere interior into three concentric zones, which differ from each other in the degree of interaction between matter and radiation. The compression wave plays a greater role in the dynamics than it does in the isotropic case. Other effects are also considered in detail.