  We study the extrapolation of nuclear shell structure to the region of
superheavy nuclei in self-consistent mean-field models -- the
Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a
large number of parameterizations. Results obtained with the Folded-Yukawa
potential are shown for comparison. We focus on differences in the isospin
dependence of the spin-orbit interaction and the effective mass between the
models and their influence on single-particle spectra. While all relativistic
models give a reasonable description of spin-orbit splittings, all
non-relativistic models show a wrong trend with mass number. The spin-orbit
splitting of heavy nuclei might be overestimated by 40%-80%. Spherical
doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or
(Z=126,N=184) depending on the parameterization. The Z=114 proton shell
closure, which is related to a large spin-orbit splitting of proton 2f states,
is predicted only by forces which by far overestimate the proton spin-orbit
splitting in Pb208. The Z=120 and N=172 shell closures predicted by the
relativistic models and some Skyrme interactions are found to be related to a
central depression of the nuclear density distribution. This effect cannot
appear in macroscopic-microscopic models which have a limited freedom for the
density distribution only. In summary, our findings give a strong argument for
(Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.
