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This paper deals with the dielectric relaxation in glycerol at different temperatures (down to 25 K) for protracted periods of time. Two relaxation maxima were observed. The peak at lower frequencies was ascribed to the relaxation alpha-process of glycerol proper; the peak at higher frequencies differed in samples from different manufacturers, so that it represents rather a relaxation peak associated with contaminants and not the true beta-process in glycerol. The alpha-process was considerably masked by the conductivity component. During a long-time exposure of glycerol to a low constant temperature, the relaxation spectrum shifts with increasing time to lower frequencies, reaching a steady position after about 20 hours.