Results of research toward measuring the neutron cross sections for nitrogen and oxygen in the neutron energy range from 4 to 12 Mev are presented. New techniques for the use of low-yield and multiple-group neutron source reactions, which were developed to perform these measurements, are shown, along with additional data obtained for the neutron source reactions Be-9 (alpha, n)C-12 and N-15 (d, n)O-16. In addition to the N-14(n, d sub O)C-13 reaction measurements, the C-13 (d, n)N-14 reaction was investigated to provide additional deuteron stripping data for evaluating the spins and parities of the lowlying states of N-14, and to provide additional information on the reaction mechanism for deuteron induced reactions. Measurements and results are given for the differential elastic, total, and nonelastic neutron cross sections for nitrogen and oxygen at several neutron energies. (Author).