Seed-blanket type nuclear reactor cores (10,100) are employed to burn thorium fuel with conventional reactor fuels, including nonproliferative enriched uranium, and weapons or reactor grade plutonium. In a first embodiment, the core (10) is completely nonproliferative in that neither the reactor fuel, nor the generated waste material, can be used to manufacture nuclear weapons. In a second embodiment of the invention, the core (100) is employed to burn large amounts of weapons grade plutonium with the thorium, and provides a convenient mechanism by which stockpiled weapons grade plutonium can be destroyed and converted into electrical energy. The cores of both embodiments are comprised of a plurality of seed-blanket units (12, 102) which have centrally located seed regions (18,104) that are surrounded by annular blanket regions (20,106). The seed regions contain the uranium or plutonium fuel rods (22,110), while the blanket regions contain thorium fuel rods (26,118). The moderator/fuel volume ratios and relative sizes of the seed and blanket regions are optimized so that neither embodiment generates waste materials that can be employed for manufacturing nuclear weapons. A novel refueling scheme is also employed with the first embodiment to maximize seed fuel utilization, and further insure that the spent fuel cannot be employed for manufacturing nuclear weapons.