The use of polarized infra-red radiation in examining the structure and orientation of high polymers has been investigated quantitatively. It is shown that infra-red spectroscopy can furnish evidence for double orientation in rolled sheets of nylon 66, polyvinyl alcohol and (with less certainty) polythene. In the case of polyvinyl formate, acetate, chloride and polyvinylidene chloride such double orientation could not be detected. Evidence is given to show that in nylon the N-H bond is bent by hydrogen bonding forces, the angle between this bond and the plane of the skeleton being thereby reduced from 39 degrees (the valency angle) to 22 degrees. The structure of polyvinyl alcohol recently proposed by Bunn receives strong support from the absence of dichroism in the O-H frequency in the spectrum of that material, when a doubly oriented specimen is examined.