  We study stability of superdeformed oblate (SDO) superheavy $Z\geq 120$
nuclei predicted by systematic macroscopic-microscopic calculations in 12D
deformation space and confirmed by the Hartree-Fock calculations with the
realistic SLy6 force. We include into consideration high-$K$ isomers that very
likely form at the SDO shape. Although half-lives $T_{1/2}\lesssim10^{-5}$ s
are calclulated or estimated for even-even spin zero systems, decay hindrances
known for high-$K$ isomers suggest that some SDO superheavy nuclei may be
detectable by the present experimental technique.
