[en] A new type of double-resonance spectroscopy of a quantum gas based on interaction-induced frequency modulation of a probe transition has been considered. Interstate interaction of multilevel atoms causes a coherence-dependent collisional shift of the transition between the atomic states |1〉 and |2〉 due to a nonzero population of the state |3〉. Thus, the frequency of the probe transition |1〉−|2〉 experiences oscillations associated with the Rabi oscillations between the states |1〉 and |3〉 under continuous excitation of the drive resonance |1〉−|3〉. Such a dynamic frequency shift leads to a change in the electromagnetic absorption at the probe frequency and, consequently, greatly enhances the sensitivity of double-resonance spectroscopy as compared to traditional “hole burning”, which is solely due to a decrease in the population of the initial state |1〉. In particular, it has been shown that the resonance linewidth is determined by the magnitude of the contact shift and the amplitude of the drive field and does not depend on the static field gradient. The calculated line shape and width agree with the low-temperature electron-nuclear double-resonance spectra of two-dimensional atomic hydrogen.