X-ray crystallographic structures of two polymorphs (alpha- and beta-forms) of 1,5-dimethylsemibullvalene-2,6-dicarbonitrile, in which the molecules undergo rapid, nondegenerate Cope rearrangement; have been obtained over the temperature range 20-295 K. CP-MAS carbon-13 NMR spectra of the beta-form have been observed over the temperature range 140-340 K. A generalized treatment for the perturbation of degeneracy has been developed and it is shown that the results of the X-ray and NMR methods are in excellent agreement. The thermodynamic parameters, Delta H-P and Delta S-P, for the perturbation of degeneracy in the beta-form are reported. A possible explanation for the difference in the magnitudes of the perturbation of degeneracy in the two crystalline forms is suggested. It is noted that for equilibrating systems, for which the barriers for interconversion are of the order of 1-10 kJ mol(-1), the transition between rapid and extremely slow equilibration occurs over a very narrow range at cryogenic temperatures, thus precluding direct observation of limiting structures.