Multiple-phonon structure has been observed in both the Raman spectrum in the exciton region and the excitation spectrum for the phonon-assisted free exciton emission of a layer semiconductor, red-HgI_2. The associated longitudinal phonon has symmetry E. Two dimensionality in its dispersion contributes to the large cross section for the multiple-phonon scattering. The multiple-phonon structure observed in the Raman spectrum suggests that the initial state for the resonant Raman scattering is given not only by the polariton state but also by the hot exciton state
