Over the past quarter century we have carried out a large number of studies of the ring- puckering vibrations of small ring-molecules. The far-infrared and Raman spectra of these large amplitude motions have been used to determine the molecular conformation and 1-D potential energy functions. The forces which are usually the principal contributors to the potential functions are the ring-angle strain and torsional forces, which often result when CH2 groups are next to each other. In the present study we have examined the far-infrared and Raman spectra of two oxygen-containing molecules which have turned out to have unusual potential energy functions. 1,3-dioxole and 4H-pyran.