Predictions of identification and production of new superheavy nuclei with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>119</mml:mn></mml:mrow></mml:math> and 120

Effective single-particle potentials obtained from the established nonrelativistic nuclear energy density functional approach are incorporated into the microscopic-macroscopic method to calculate the ground-state shell corrections, mass excesses, and ${Q}_{\ensuremath{\alpha}}$ values for heaviest nuclei. The low-lying one-quasiparticle states are studied in the isotonic chains with neutron numbers $N=175$, 176, and 177. The isomeric states are discussed in the odd isotopes. The possible $\ensuremath{\alpha}$-decay chains of nuclei $^{295}119$ and $^{295,297}120$ are analyzed and compared with the available experimental data. The termination of the $\ensuremath{\alpha}$-decay chains by spontaneous fission is analyzed. The production cross sections are calculated for superheavy nuclei with $112\ensuremath{\le}Z\ensuremath{\le}120$ in the actinide-based complete fusion reactions with projectiles $^{48}\mathrm{Ca}, ^{48,50}\mathrm{Ti}, ^{54}\mathrm{Cr}, ^{58}\mathrm{Fe}$, and $^{64}\mathrm{Ni}$.

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