The shell structure of superheavy nuclei is investigated within variou
s parameterizations of relativistic and nonrelativistic nuclear mean-f
ield models. The heaviest known even-even nucleus (264)(156)Hs(108) is
used as a benchmark to estimate the predictive value of the models. F
rom 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 parametrizatio
n.