[en] The narrow-gap II-VI and IV-VI alloys are convenient objects for studying the electron-phonon interaction. However, the concentration of free carriers in the IV-VI alloys is rather high (∼10¹⁸ cm^-3), which complicates studying this effect, by the optical reflection method. The concentration of free carriers in the narrow-gap Hg_1-xZn_xTe alloys is considerably lower (∼10¹⁶ cm^-3). Therefore, the plasma component exerts less effect on the lattice reflection spectrum. The reflection spectra of Hg_1-xZn_xTe crystals with x = 0.1-1 were studied in the far-IR region in the range of 30-700 cm^-1 at 40-300 K. Using the dispersion analysis and the Kramers-Kronig method, the frequencies of the TO phonons of the HgTe-like and ZnTe-like modes were determined depending on the composition. It is shown that the reconstructed phonon spectrum involves two modes. The temperature dependences of the frequencies of the TO phonons and the damping parameter were measured for the narrow-gap alloy with x = 0.1 in the range of 80-200 K. A decrease in the frequency of the TO phonon of the soft mode in the vicinity of the inversion point of the bands at T = 110 K was for the first time found by optical methods. The damping parameter slightly increases in the vicinity of this temperature. The result obtained qualitatively agreed with the theoretical model of Kawamura et al., which makes allowance for the effect of the electron-phonon interaction on the frequency of the soft mode in the IV-VI compounds