Possible contributions of electron-magnon scatterings for the ultrafast demagnetization after femtosecond laser irradiation of films of Ni and Fe are investigated by the ab initio spin-density-functional electron theory. The calculations are based on Fermi's golden rule for transition rates, and the nonequilibrium after the action of the laser pulse is modeled by different chemical potentials for electrons which are in a ``dominant spin-up'' or in a ``dominant spin-down'' state. First, it is shown that the experimentally observed demagnetization cannot be described by electron-magnon spin-flip scatterings with concomitant changes of the electronic orbital moments which are immediately quenched by the crystal field, a mechanism which has been suggested by Carpene et al. Second, it is argued that the experimentally observed demagnetization possibly can be explained by a combination of individual spin-flip electron-phonon and spin-flip electron-magnon processes. A precondition for this is (among others) that the magnon emission rate is much larger than the magnon absorption rate. It is shown that this precondition is indeed fulfilled for Ni and especially for Fe.