N-methylacetamide may be viewed as a simple model for polypeptides. Unusual intensities have previously been observed in its amide vibrational spectra and were attributed to contradictory causes, namely, Fermi resonance, vibrational polarons, and dynamic proton transfer along the H bond. We report the first inelastic neutron scattering study of three specifically deuterated derivatives at different temperatures along with new infrared spectra. The analysis of the librations in the INS spectra indicates a degeneracy between the N-CH3 methyl torsional mode and another degree of freedom assigned to one component of the skeletal torsion. No direct evidence for a methyl-methyl coupling is observed. However gamma(CO) appears strongly coupled to the motions of the neighboring C-CH3 group. A new absorption band ("X") is observed at approximately 1590 cm(-1) in the IR spectrum of the amide-1/amide-2 region. This calls into question the previous assignment of a band at similar to 1600 cm(-1) as the overtone of gamma(NH). In addition, all observed peaks in the amide-2 region shift to higher frequency on cooling so that none of them could be assigned to the nu(NH) mode, as previously proposed. Previous theoretical explanations of the anomalous amide spectra of N-methylacetamide based on either Fermi resonance or the proton-transfer model are therefore in disagreement with our new experimental data.