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We have explored the occurrence of the spherical shell closures for superheavynuclei in the framework of the relativistic Hartree–Fock–Bogoliubov (RHFB) theory.Shell effects are characterized in terms of two-nucleon gaps δ2n(p).Although theresults depend slightly on the effective Lagrangians used,the general set of magicnumbers beyond 208Pb are predicted to be Z = 120,138 for protons and N = 172,184,228 and 258 for neutrons,respectively.Specifically the RHFB calculations favor thenuclide 304120 as the next spherical doubly magic one beyond 208Pb.