Abstract: A process for the separation of substances hindering the recovery of the fissionable materials uranium and plutonium and for the separation of the fissionable materials to be recovered in a reprocessing process for spent, irradiated nuclear fuel- and/or fertile materials. A second and a third wash of the organic phase is performed for residual ruthenium separation and residual zirconium separation, and there is a repetition of the Pu stripping step with simultaneous electrolytic reduction of Pu(IV) to Pu(III). The second and third wash solutions or the aqueous phase employed for the repetition of plutonium stripping, respectively, each contains a high concentration of product uranyl nitrate. The aqueous run-off from the second and third washes and from the repetition of the Pu stripping step is indirectly fed back into the aqueous fuel solution employed in the first extraction step of the reprocessing method by first feeding these run-offs to an intermediate treatment.