Configuration-constrained potential-energy-surface calculations are performed including β 6 deformation to investigate high-K isomeric states in nuclei around 254 No and 270 Ds, the heaviest nuclei where there have been some observations of two-quasiparticle isomers, while data for four-quasiparticle isomers are scarce. We predict the prevalent occurrence of four-quasiparticle isomeric states in these nuclei, together with their favored configurations. The most notable examples, among others, are K π = 20 + states in 266,268 Ds and 268,270 Cn having very high K value, relatively low excitation energy, and well-deformed axially symmetric shape. The predicted isomeric states, with hindered spontaneous fission and α decay, could play a significant role in the future study of superheavy nuclei. One of the important endeavors in current nuclear-structure studies is to extend the nuclide landscape towards the predicted island of stability of superheavy nuclei and beyond, which will provide us with knowledge about the end of the periodic table of elements, the heaviest magic numbers in nuclei, and the nuclear mass limit [1,2]. When going far away from 208 Pb towards the expected superheavy doubly magic nucleus, nuclear shape significantly deviates from spherical symmetry. The nuclei around 254 No and 270 Ds are predicted to be well deformed with non-negligible higher-order deformation such as β 6 [3][4][5][6]. Modern spectroscopy experiments (see Refs. [7][8][9] and references therein) have been able to study these nuclei in detail. Together with various model calculations (see, e.g., Refs. [10-27]), such studies of collective and singleparticle excitations result in not only insights into these nuclei themselves but also information for the heavier unknown nuclei due to the contributions of higher-lying single-particle states. Amongst them, multiquasiparticle (multi-qp) isomers associated with axial symmetry and nearly pure Nilsson configurations provide structure information in a very direct way.This type of isomer [28] occurs in axially deformed nuclei through unpaired nucleons occupying single-particle states with high-values ( is the single-particle angular momentum projection onto the symmetry axis). The total angular momentum along the symmetry axis, K, is therefore high, and leads to retardation in γ -ray transitions to low-K states. Since the conservation of the K quantum number is intimately related to axial symmetry, the observations of high-K isomers in nuclei around 254 No and 270 Ds [7] support the predictions of well-developed prolate deformations for the nuclei. These nuclei, with high-orbitals around the Fermi surfaces for both neutrons and protons, are analogous to the A ≈ 180 nuclei and neutron-rich Hf nuclei where not only two-qp but also four-qp (or more) high-K isomers prevail [29][30][31]. Indeed, it has been observed in 254 254 No is so far the unique four-qp isomer known in transfermium nuclei. More could be found with the advance of experimental techniques applicable to the heaviest...