  Two-quasiparticle bands and low-lying excited high-$K$ four-, six-, and
eight-quasiparticle bands in the doubly-odd ${}^{174, 176}$Lu are analyzed by
using the cranked shell model (CSM) with the pairing correlations treated by a
particle-number conserving (PNC) method, in which the blocking effects are
taken into account exactly. The proton and neutron Nilsson level schemes for
${}^{174, 176}$Lu are taken from the adjacent odd-$A$ Lu and Hf isotopes, which
are adopted to reproduce the experimental bandhead energies of the
one-quasiproton and one-quasineutron bands of these odd-$A$ Lu and Hf nuclei,
respectively. Once the quasiparticle configurations are determined, the
experimental bandhead energies and the moments of inertia of these two- and
multi-quasiparticle bands are well reproduced by PNC-CSM calculations. The
Coriolis mixing of the low-$K$ ($K=|\Omega_1-\Omega_2|$) two-quasiparticle band
of the Gallagher-Moszkowski doublet with one nucleon in the $\Omega = 1/2$
orbital is analyzed.
