We have carried out a study of superheavy nuclei in the framework of t
he relativistic mean-field theory. Relativistic Hartree-Bogoliubov (RH
B) calculations have been performed for nuclei with large proton and n
eutron numbers, A finite-range pairing force of Gogny type has been us
ed in the RHB calculations. The ground-state properties of very heavy
nuclei with atomic numbers Z = 100-114 and neutron numbers N = 154-190
have been obtained. The results show that in addition to N = 184 the
neutron numbers N = 160 and N = 166 exhibit an extra stability as comp
ared to their neighbors. For the case of protons the atomic number Z =
106 is shown to demonstrate a closed-shell behavior in the region of
well deformed nuclei about N = 160. The proton number Z = 114 also ind
icates a shell closure, Indications for a doubly magic character at Z
= 106 and N = 160 are observed, Implications of shell closures on a po
ssible synthesis of superheavy nuclei are discussed.