A hydrosol containing, in nitrate form, a fuel or fuel-and-breeder material which is projected horizontally in the form of droplets into a gas phase containing gaseous ammonia and allowed to fall in a drip-casting column into a precipitation bath containing ammonium hydroxide. In the gas phase, the droplets are hardened just enough to prevent their deformation upon penetrating into the precipitation bath where the hardening is completed. A falling height of 5 cm is suitable. The granules are washed free of ammonium nitrate, then dried, and then sintered. The heavy metal content in the hydrosol is between 1.5 and 3 moles per liter, and the pH value of the precipitation bath is between 8 and 9. The hydrosol contains the heavy metal in oxide form and the process can be used with a thorium oxide hydrosol or a hydrosol that, in addition to thorium oxide, contains the oxide of hexavalent uranium, in the latter case the hexavalent uranium being present in a proportion up to 25% by weight of the total heavy metal. The process is also applicable to producing kernels of mixed thorium and plutonium oxides. In the case of uranium-containing granules, the sintering step is carried out in a reducing atmosphere to convert the uranium to the tetravalent state.