The thermal stability of a collisional, radiating edge plasma in magnetic confinement experiments with respect to marfe-type perturbations is investigated analytically and numerically. The fluid description used includes a non-local electron heat flux model and non-equilibrium impurity radiation cooling. The dispersion relation of a homogeneous plasma is derived analytically, and stability criteria are given. Various experimental scenarios are simulated with a sophisticated numerical model including all the relevant dynamics along field lines and a rough approximation of cross-field transport. The formation and history of global 'marfes' and the onset of relaxation oscillations under appropriate conditions are demonstrated. The possible occurrence of more localized perturbations is discussed. The results compare well with those of experiments.