[en] The radiative strength functions for the partial transitions from neutron resonances to the ground and low-lying states of odd-A spherical nuclei are calculated within the quasiparticle-phonon nuclear model. The fragmentation of one-quasiparticle and quasiparticle plus phonon state is calculated. This allowed one to calculate γ- transitions between the one-quasiparticle components (valence transitions) and γ-transitions between the quasiparticle plus phonon and one-quasiparticle components of the wave functions. The energy dependence of the strength functions B(E1, eta) and B(M1, eta) is calculated near binding energy Bsub(n) for ⁵⁵Fe and sup(59,61)Ni. The corresponding experimental data are described qualitatively. The contribution of the valence E1-transitions to the strength function is shown to be from 20% to 90% and of M1-transitions about 1%. The influence of the M1 giant resonance is important for M1 transition probabilities