The energy distribution of a monoenergetic incident neutron beam after a single scattering event provides information concerning the molecular motions of a polymer in the region 800 to 30 cm−1. In polyethylene (Marlex 6050) several peaks are observed in the neutron spectrum between 200 and 600 cm−1. The frequencies corresponding to these peaks are in good agreement with those predicted from a calculation of the dispersion relations of the skeletal modes (bending and stretching) taking into account interchain forces. In the case of an oriented sample of the polymer, a polarization effect can be obtained by placing the momentum transferKof the neutron parallel or perpendicular to the chain directionS.This allows the identification of transverse and longitudinal modes of vibration. This effect has been studied in the case of polyethylene and polyoxymethylene. The frequency distribution of phonons, derived from the neutron data under certain approximations, were also obtained from samples of polyoxymethylene, polyacrylonitrile, and polyethylene glycol. These results are compared with the observed infrared and the calculated frequencies.