A shutdown cooling system for a nuclear reactor operates during lapse of normal power and emergency power and has an independent power source fo removing residual heat while cooling the seals of the main reactor coolant pump. A high pressure pump delivers cooling water to the reactor cooling pump seals, a low pressure pump circulates core coolant, and a cooling mechanism discharges the decay heat. Electrical power for the pumps and associated valves and controls is provided by a dedicated power source apart from the regular residual heat removal apparatus of the reactor, and apart from the emergency generators provided for regular power failure backup.