The differential cross sections for elastic scattering of 14-Mev neutrons from nitrogen and oxygen were measured in the angular range from 17 to 140 deg , using liquid targets and annular ring geometry. Inelastic scattering to the 2.31 and 3.95-Mev levels in N/sup 14/ and to the levels near 6 and 7 Mev in O/sup 16/ was investigated over a more restricted angular range. The 2.31-Mev level in N/sup 14/ was not excited appreciably, in disagreement with previously reported results. For both elements, the elastic scattering cross sections (determined to an accuracy of 10%) were found to be appreciably higher than the optical model predictions by Rjorklund and Fernbach for scatterirg angles larger than 70 deg . The inelastic cross sections measured are, within experimental accuracy, the same as the corresponding (p,p') cross sections. (auth)