Both linear and nonlinear analysis are used to gain a better understanding of the effects of multi-dimensional transfer of energy by radiation in spatially structured stellar atmospheres. Information on the radiative response of RE (radiative equilibrium) model atmospheres to temperature fluctuations is obtained. Whether or not such perturbed systems always return to their initial RE configurations is addressed by investigation of the dependence of the radiative relaxation times on the geometry and structural lengths of the perturbations, as well as establishing the conditions under which radiative instabilities can be possible.