The infrared and far-infrared absorption spectra of β-GaSe and GaS have been measured in the temperature range from 50 to 300°K for the radiation polarized perpendicular to the c-axis in the hexagonal layer structure of these compounds. The reststrahlen frequencies measured at room temperature are 211.0 cm^ in β-GaSe and about 310 cm^ in GaS, respectively. In addition, the weak absorptions in the wave number range from 400 cm^ to 750 cm^ are identified with the multiphonon absorptions in the light of group theoretical analysis and of the experimental results on the Raman effect and on the electro-luminescence available up to date. The absorption line at 512 cm^ and band around 450 cm^ in β-GaSe are explained in terms of the localized mode of lattice vibrations induced possibly by an oxygen impurity. This analysis is the first preliminary investigation on the localized mode in a diatomic crystal of hexagonal structure
