Spectroscopic properties of 23 odd nuclei within and around the actinide region have been calculated according to a rotor plus quasiparticle approximation where the quasiparticle states have been extracted from self-consistent calculations discussed in a previous paper. The phenomenological parameters are only six force parameters fitted once for all to nuclear saturation properties, neutron and proton pairing gaps uniquely given by odd-even mass differences, and experimental ground band energies of neighboring nuclei. Excluding thus any elusive ad hoc parameter adjustment, this approach has successfully reproduced most of the experimentally confirmed rotational bands for both odd-neutron (thorium, uranium, and plutonium) and odd-proton (actinium, protactinium, neptunium, and americium) isotopes, assessing thus the validity of the whole approach and, in particular, the relevance of the self-consistent deformed mean fields yielded by the Skyrme SIII effective force. Many bands previously assigned to be of a particle-vibration nature have not been found in our calculations. Their nonrotational character is thus confirmed. Reduced transition probabilities and static moments for E 2 and M 1 electromagnetic modes have been evaluated. Calculated magnetic and electric quadrupole moments have been shown to reproduce very well available data. Absolute intraband and interband E 2 and M 1 reduced transition probabilities have also been found in very good agreement with experimental results.