Long-wave IR transmission spectra of crystal KTm(MoO<sub>4</sub>)<sub>2</sub> have been measured in polarized light (Е║а and Е║с) at T=6К in the energy range 10-40 cm<sup>-1</sup>. Two vibration modes with energy 18.5 cm<sup>-1</sup> in polarization Е║а and with energy 25.5 cm<sup>-1</sup> in polarization Е║с have been found. The structure of low-frequency vibration spectrum in the Brillouin zone was calculated using a one-dimensional model. The dependences of microwave radiation transmission in crystal KTm(MoO<sub>4</sub>)<sub>2</sub> on the external magnetic field were measured in the frequency range 90-333 GHz at low temperatures (Т=2K). It is revealed that in addition to the absorption band caused by the excitation of Tm<sup>3+</sup> ions from the ground state to the first Stark level, the transmission spectrum contains peaks in the form of sidebands. This structure is assumed to result from the dynamic coupling between the low-energy electron excitation of Tm<sup>3+</sup> ions and the acoustic vibrations of the crystal lattice.