The odd-Z 251Md nucleus was studied using combined γ-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 γ−γ 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 ≃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 gK=0.69+0.19−0.16 for the ground-state band. The odd-Z 249Md was studied using γ-ray in-beam spectroscopy. Evidence for octupole correlations resulting from the mixing of the Δl=Δj=3 [521]3/2− and [633]7/2+ Nilsson orbitals were found in both 249,251Md. A surprising similarity of the 251Md ground-state band transition energies with those of the excited band of 255Lr 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.