The dielectric spectra up to frequencies of 1 GHz of the substances 2,2-dimethyl-1,3-propanediol (or neopentylglycol, NPG) and 2-amino-2-(hydroxymethyl)-1,3-propanediol (or tris(hydroxymethyl)aminomethane, TRIS) have been determined in the orientationally disordered FCC and BCC phases respectively, in the ranges 305 - 353 K for NPG and 343 - 375 K for TRIS (in this case, in the supercooled BCC orientationally disordered phase). The dielectric relaxation of both substances has been studied by considering modified Debye theories as well as the Jonscher equation. Significant deviations from the single Debye relaxation were found in both cases. The temperature dependence of the relaxation time, assuming Arrhénius or Eyring activation models, allows one to evaluate of the activation enthalpies and entropies. Large values were obtained for both parameters, showing that there are strong intermolecular interactions via hydrogen bonds, as had been proved previously for solid phases of alicyclic and branched (tetrahedral molecules) alcohols.