A new type of resonant phenomena in the Mössbauer spectroscopy of soft magnetic materials in radiofrequency (rf) magnetic fields is predicted for the rf field frequencies related to those of components of the magnetic hyperfine structure via the parametric resonance condition. Resonant effects of this kind are still unknown in physics; they are realized not at frequencies of transitions between the energy sub-levels of the ground or excited nuclear states, which take place in conventional nuclear magnetic resonance, but at frequencies which are a combination of the frequencies of hyperfine transitions. In this case a separation between the real energy levels can exceed the value of the `resonant' frequency by about 10 orders of magnitude and the resonant rf field sets as if in coherency between these energy levels. Such resonances can only be observed when relaxation processes play an essential role, which permits them to be defined as the relaxation-stimulated resonances. The simplest relaxation model of so-called one-way and localized relaxation is proposed. Within this model an analytical expression for Mössbauer absorption spectra is derived, based on which the specific features of the new resonant effects are analysed in detail.