A method and an arrangement for producing spherical fuel cores and/or breeder material cores by dripping a pouring solution containing uranyl nitrate and a solution containing at least one auxiliary agent into an ammoniacal precipitation bath to form microspheres, aging, washing, drying, and thermally treating the microspheres. In order to provide a continuous production method along with a constantly high core quality, it is proposed that 1) the microspheres from the precipitation bath be separated through a first separator and fed to the ammoniacal aging water for aging, 2) the contact duration of the microspheres with the liquid of the precipitation bath before being introduced into the aging water be set equally or substantially equally, 3) the microspheres be transferred from the aging water to a multi-stage cascade scrubber using a transfer device, wherein the microspheres are washed in the multi-stage cascade scrubber so as to be free or substantially free from ammonium nitrate and at least one auxiliary agent contained in the microspheres, and 4) after drying, the microspheres be calcinated while distributed in a monolayer during a thermal treatment.