Abstract: Spent reactor fuel elements are dissolved in dilute nitric acid. After addition of acetic acid as a complexing agent, the nitric acid is partly decomposed and the mixture subjected to electrolysis while a carrier liquid, which may be dilute acetic acid or a dilute mixture of acetic acid and nitric acid is caused to flow in the electric field between the electrodes either against the direction of ion migration or transversely thereto. The ions of uranium, plutonium and other transuranium elements, and of fission products accumulate in discrete portions of the electrolyte and are separately withdrawn as at least three fractions after one or more stages of electrolysis.