We report Mössbauer measurements of Fe1857Ni82 permalloy under the influence of an external radio-frequency (rf) magnetic field. Measurements were performed in both energy and time domain. Line splitting caused by direct coupling of the rf field to the nuclear spin manifolds was seen in the energy domain measurements. First observations of the time development of Mössbauer absorption in Fe57 under rf magnetic excitation at specific constant Doppler velocities were also made. A π/2 phase change was observed in the absorption time dependence when measurements were performed on opposite slopes of a Mössbauer resonance line. A maximum frequency limit, above which the sample foil no longer exhibited a coherent response to the rf excitation, was observed. We also present a detailed description of an application of the density matrix theory to the analysis of the Mössbauer spectra.