  The odd-$Z$ $^{251}$Md nucleus was studied using combined $\gamma$-ray and
conversion-electron in-beam spectroscopy. Besides the previously observed
rotational band based on the $[521]1/2^-$ configuration, another rotational
structure has been identified using $\gamma$-$\gamma$ coincidences. The use of
electron spectroscopy allowed the rotational bands to be observed over a larger
rotational frequency range. Using the transition intensities that depend on the
gyromagnetic factor, a $[514]7/2^-$ single-particle configuration has been
inferred for this band, i.e., the ground-state band. A physical background that
dominates the electron spectrum with an intensity of $\simeq$ 60% was well
reproduced by simulating a set of unresolved excited bands. Moreover, a
detailed analysis of the intensity profile as a function of the angular
momentum provided a method for deriving the orbital gyromagnetic factor, namely
$g_K = 0.69^{+0.19}_{-0.16}$ for the ground-state band. The odd-$Z$ $^{249}$Md
was studied using $\gamma$-ray in-beam spectroscopy. Evidence for octupole
correlations resulting from the mixing of the $\Delta l = \Delta j = 3$
$[521]3/2^-$ and $[633]7/2^+$ Nilsson orbitals were found in both
$^{249,251}$Md. A surprising similarity of the $^{251}$Md ground-state band
transition energies with those of the excited band of $^{255}$Lr has been
discussed in terms of identical bands. Skyrme-Hartree-Fock-Bogoliubov
calculations were performed to investigate the origin of the similarities
between these bands.
