Isothermal dielectric relaxation measurements were carried out on xylitol and threitol. These, together with existing data on sorbitol and glycerol, enabled us to identify the general features in the frequency dispersion and the changes when increasing the number of carbon atoms in the molecule in these polyalcohols. These features are interpreted in the framework of the coupling model. In sorbitol, xylitol, and threitol, the Johari-Goldstein beta-relaxation peaks at a frequency, nu(beta), near the independent relaxation frequency, nu(0), obtained from calculations using the coupling model. This coincidence indicates that the Johari-Goldstein beta-relaxation is the precursor to the cooperative structural alpha-relaxation. For glycerol and for some nonassociating glass-formers, which have no resolved Johari-Goldstein beta-relaxation peak because nu(0) is too close to the alpha-relaxation peak frequency, a near-constant loss (NCL) contribution can be seen at frequencies much higher than nu(0). Evoking the physical meaning of nu(0), this ubiquitous feature in the dielectric spectra leads to a description of the evolution of the molecular dynamics from the short time regime, when essentially all molecules are caged (i.e., the NCL regime), to the intermediate time regime defined by 1/2pinu(0) (or by 1/2pinu(beta) if the glass-former has a resolved Johari-Goldstein beta-relaxation), and to the long time regime when all molecules participate in the fully cooperative structural alpha-relaxation described by the Kohlrausch function.