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 \(5211/2^-\) 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 \(5147/2^-\) 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 \(\Delta l = \Delta j = 3\) \(5213/2^-\) and \(6337/2^+\) 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.