  The shell structure of superheavy nuclei is investigated within various
parametrizations of relativistic and nonrelativistic nuclear mean field models.
The heaviest known even-even nucleus 264Hs is used as a benchmark to estimate
the predictive value of the models. From that starting point, doubly magic
spherical nuclei are searched in the region Z=110-140 and N=134-298. They are
found at (Z=114, N=184), (Z=120, N=172), or at (Z=126, N=184), depending on the
parametrization.
