Previous dielectric relaxation measurements of glycerol and propylene carbonate and new results on propylene glycol performed below the conventional glass transition temperatures T g after long periods of aging all show that the excess wing ͑a second power law at higher frequencies͒ in the isothermal dielectric loss spectrum, develops into a shoulder. These results suggest that the excess wing, a characteristic feature of a variety of glass-formers, is the high frequency flank of a JohariGoldstein -relaxation loss peak submerged under the ␣-relaxation loss peak. With this interpretation of the excess wing assured, the dielectric spectra of all three glass-formers measured at temperatures above T g are analyzed as a sum of a ␣-relaxation modeled by the Fourier transform of a Kohlrausch-Williams-Watts function and a -relaxation modeled by a Cole-Cole function. Good fits to the experimental data have been achieved. In addition to the newly resolved -relaxation on propylene glycol, the important results of this work are the properties of the -relaxation in this class of glass-formers in the equilibrium liquid state obtained over broad frequency and temperature ranges.