Abstract: In the method of shutting down a high temperature nuclear reactor having a negative temperature coefficient of reactivity, such as a gas cooled pebble-bed nuclear reactor, while the core is operating in the critical state with the core having a predetermined critical average core temperature and with the heat generated in the critical state being removed by a coolant, effecting the shut down by reducing or discontinuing the removal of heat from the reactor core and increasing the average core temperature by an amount above the critical average core temperature for rendering the core hot sub-critical due to the negative temperature coefficient of reactivity. The core can be maintained in the hot sub-critical state by a controlled removal of after shut-down heat from the core.