A nuclear steam supply system having a shutdown system for removing residual decay heat generated by a nuclear fuel core. The steam supply system may utilize gravity-driven primary coolant circulation through hydraulic-ally interconnected reactor and steam generating vessels forming the steam supply system. The shutdown system may comprise primary and secondary coolant systems. The primary coolant cooling system may include a jet pump comprising an injection nozzle disposed inside the steam generating vessel A portion of the circulating primary coolant is extracted, pressurized and returned to the steam generating vessel to induce coolant circulation under reactor shutdown conditions. The extracted primary coolant may further be cooled before return to the steam generating vessel in some operating modes. The secondary coolant cooling system includes a pumped and cooled flow circuit operating to circulate and cool the secondary coolant, which in tun extracts heat from and cools the primary coolant.