The [1,9] sigmatropic rearrangement has been studied by Dynamic NMR spectroscopy for two 2-acyloxyuopone mesogens and for 2-acetyloxytropone. The proton spectra of the compounds in CDCl3 have been recorded in the range 213-328 K and the rate constants for the dynamic process determined by line-shape analysis. Evidences of the same rearrangement were found in the H-2 NMR spectra of the three molecules in the nematic phase E63 between 293 and 350 K. Values of the rate constants were yielded also by 2D-exchange spectra in the slow rate limit (300-320 K). The trends of the kinetic constants against temperature, analyzed by the Eyring equation, give the activation parameters of the rearrangement. The activation energies in the nematic solvent are slightly higher than the corresponding ones in CDCl3. By extrapolating these results, we can infer a range of values for the frequency of the process in the liquid-crystalline phases of compounds I and II.