  We have explored the occurrence of the spherical shell closures for
superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov
(RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps
$\delta_{2n(p)}$. Although the results depend slightly on the effective
Lagrangians used, the general set of magic numbers beyond $^{208}$Pb are
predicted to be $Z = 120$, $138$ for protons and $N = 172$, 184, 228 and 258
for neutrons, respectively. Specifically the RHFB calculations favor the
nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb.
Shell effects are sensitive to various terms of the mean-field, such as the
spin-orbit coupling, the scalar and effective masses.
