Deuterium NMR spin-lattice relaxation times (T-1Z) of N-deuterated microcrystalline secondary amides vary from less than 1 s to more than 500 s at room temperature. The main motion effecting relaxation is an out-of-plane libration of the amide, as indicated by temperature-dependent line shapes and anisotropic relaxation spectra. Over 25 amides were measured; they vary with respect to side chain sterics, hydrogen bond lengths, hydrogen bond geometry, and crystal packing, The temperature-dependent deuterium line shape and anisotropic relaxation rates indicate an out-of-plane angular deflection of approximately 10 degrees; the angle is probably similar for the rapidly and slowly relaxing amides, while the apparent time constant for the motion probably varies dramatically. Deuterons in methylene groups on both sides of the amide group for caprylolactam and caprolactam also indicate an out-of-plane libration with relaxation rates faster than that of the amide deuteron, probably because the angular extent of the distortion is greater for the flanking alpha-deuteron than for the amide deuteron. Carbon relaxation measurements on lauryllactam indicate that the whole molecule librates to a comparable extent. Temperature-dependent relaxation rates for caprylolactam and caprolactam showed non-Arrhenius monotonic increases in the relaxation rates with increasing temperature, as expected for libration dynamics; furthermore the quadrupolar relaxation measurements support the assumption that the dominant spectral density contribution is above the Larmor frequency (i.e. T-1Q is longer than T-1Z). In aggregate, the data indicate that the motion effecting amide relaxation is a low-amplitude libration involving the entire molecule. Previous work on the librations of amides suggested that these librations are pronounced on the NMR time scale when the substance is near a phase transition; we report here that there is additionally a relation between the extent of libration and the structure. Comparison of the relaxation times to structures indicates that only amides with flanking alkyl groups on both sides (larger than a methyl group) exhibit extensive libration; furthermore only those amides with both flanking dihedral angles, phi {C2C1-NC(=O)} and psi {N(O=)C-C1＇C-2＇}, near -60 degrees (similar to+/-40 degrees) have fast spin-lattice relaxation. On the other hand, correlation between the deuterium relaxation times and hydrogen bond length nor geometry nor crystal packing was observed. Variation in the electronic structures of the conjugated amide groups was indirectly probed by measuring the chemical shift anisotropy of the amide carbonyl carbon, the deuterium quadrupolar coupling constant, and vibrational frequencies. These parameters did not vary dramatically, indicating that the electronic structure is not strongly variable; the modest variation did not correlate with deuterium relaxation rates. The chemical shift tensor elements were delta(11) = 91.4 +/- 5, delta(22) = 185 +/- 8, and delta(33) = 245 +/- 3 ppm, the quadrupolar coupling constant and its anisotropy were 203 +/- 10 kHz and 0.15 +/- 0,02, the NH stretch frequency was 3300 +/- 42 cm(-1), and the carbonyl stretch frequency was 1644 +/- 25 cm(-1). We suggest a model in which the shape of the local potential associated with flanking alkyl groups leads to "overdamping" of the amide Librational mode and generates slower (nanosecond) components in the vibrational frequency spectrum.