A cholesteryl hydrogen phthalate (CHP) and its complex salts with normal aliphatic amines (C-n-amines) are capable of forming a glassy liquid-crystalline phase, where an anisotropic organization of their fluid mesophase is frozen in an uncrystallized solid state. Differential scanning calorimetry (DSC) measurements were conducted for these glassy materials to examine an enthalpy relxation phenomenon, occurring when they were annealed adequately at temperatures lower than the glass transition temperature. The enthalpy relaxation behavior, monitored as evolution of a DSC endothermic peak, was analyzed in terms of a Kohlrausch-Williams-Watts type of stretched exponential equation, and the overall relaxation time tau and a parameter beta chracterizing the distribution of the relaxation mode were evaluated. It turned out that the tau values obtained for CHP/C-n-amine salts were rather smaller than those for CHP per se, and beta became close to unity when CHP was complexed with the C-n-amines through ionic interaction, the latter component employed having 12, 16, and 18 carbons. The activation energy for the relaxation process of the CHP/C-n-amine samples was considerably small, compared with that in the case of CHP alone, and tended to decrease with an increase in the carbon number of the amine component. An attempt was also made to estimate the fragility of these samples as glass.