This paper deals theoretically with a radial fuel shuffling problem for an accelerator driven transmuter (ADT), which is similar to the concept of critical traveling wave reactor (TWR). The problem is formulated as a nonlinear eigenvalue problem based on the one-group diffusion theory, the macroscopic cross sections being approximated as functions of neutron fluence. A 2-D cylindrically symmetric core is considered and a discrete radial serial fuel shuffling scheme is modeled theoretically as a continuous process. Variations in mixed Uranium-Minor Actinide (U-MA) oxide fuel isotopic compositions fed in a lead cooled reactor are investigated numerically. It is shown that there are asymptotic (TWR) modes for certain fresh fuel compositions corresponding to certain eigenvalue k(eff) and fuel drift speed. Up to about 40% MA content of total heavy metal (U + MA) k(eff) reaches a value being slightly less than unity. The aim of this study is not to predict accurate results for a certain core design and fuel reloading scheme, but to show the existence of such fuel shuffling modes in an idealized TWR case. The showed possibility that the TWR charged with oxide fuel can be driven by an accelerator to destroy MAs by a large amount is of high interest for transmutation. Copyright (C) 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.