The general laws governing the increase in xenon and iodine concentration in nuclear reactors employing thermal neutrons are given on the assumption that the neutron flux in the core is uniform. The authors show how the progressive xenon poisoning enables the imposition of certain rates of radioactive liberation on the control rods (insertion and withdrawal speeds). Since the progress in xenon poisoning depends on the past history of the reactor and since the search for the most rapid shut-down procedure is really a question of finding the best solution, a certain number of parameters have been evaluated which enable a definition of the shut-down procedure of high flux reactors to be stated which takes into account the progress in xenon concentration and the amount of available radioactivity. The results of the calculations have been applied to high flux reactors of the type Siloë and Pegase.