Wave fields, which are described mathematically by higher order Bessel functions, carry an orbital angular momentum and thus represent particular types of optical vortex beams with helical wavefronts. For the generation of such vortex beams, one may use, for instance, diffractive spiral axicons. Diffraction, however, leads invariably to strong dispersion, which is detrimental for ultrashort pulses since it leads to severe pulse broadening. This pulse broadening can be minimized or reduced completely (at least, in a specific plane of propagation) if the pulses propagate additionally through a medium with normal refractive dispersion. The refractive-diffractive generation of ultrashort vortex pulses was demonstrated earlier for a pulse duration of approximately 8 fs [Opt. Lett.37, 3804 (2012)10.1364/OL.37.003804OPLEDP0146-9592]. Here, we present an analytical description of the generation and propagation of these vortex beams and of the refractive-diffractive compensation of the dispersion.