Analysis of neutron-capture cross sections in the resolved resonance range reveals that a large fraction of them (13 of 21, or 62%) exhibit highly significant (>99.9% confidence level) oscillations about their average value. Oscillations exceed a significance level of 5σ in nine cases (43%). Oscillations comprise 10.86±0.64% of the average cross section with periods ranging from 68.2 to 2380 eV. This contradicts random matrix theory (RMT), which predicts that fluctuations about the average cross section should be entirely random and demonstrates that deviations from RMT are common and widespread in neutron-capture data. These facts suggest there is a widespread physical mechanism that is missing from current nuclear physics models describing neutron-capture cross sections.