Proton magnetic resonance relaxation times for liquid and supercooled glycerol of low water content have been measured in the temperature range 200°K to 435°K. The spin-lattice relaxation times differ substantially from the earlier measurements.The results are used to deduce correlation frequencies for motion of the glycerol molecules and these are compared with correlation frequencies deduced from dielectric and ultrasonic measurements. Values are now available in the range 10^-1 to 2 × 10¹⁰ c/s which is almost the complete temperature range, glass point to boiling point. Some indication is found that translational molecular motion may be faster than rotational motion in liquid glycerol and possibly dipolar reorientation is faster than that of the whole molecule. Several difficulties in the interpretation are encountered which are no doubt connected with the hydrogen bonding in liquid glycerol. A distribution of correlation frequencies of an extent depending on the temperature is required. The dielectric internal field correction is discussed.