The elimination of transuranium (TRU) elements by neutron absorption has been investigated in an actual power liquid-metal fast breeder reactor (LMFBR) (of the Superphenix type). Special fuel elements containing TRU oxides were considered in different core locations. The effects on design parameters have also been evaluated. The results show that the advantages of TRU elimination by means of LMFBRs, compared with using a thermal reactor, consist mainly of the small perturbation of the integral properties and design parameters of the reactor for the large amount of TRU that can be introduced. However, from the point of view of the TRU transmutation reaction rates, thermal reactors seem to be better. The choice of a compromise between the variation of design parameters and the TRU amount to be transmutated depends on the actual reactor design.