Fast pulse methods have been used to study the drift mobility of both electrons and holes in pure CdS crystals, obtained from different sources, over the temperature range 500°K - 77°K. An electron pulse of 5 nsec. duration generates free carriers near the top electrode, and measurements of the transit time in a pulsed applied field lead to a value for the drift mobility. The method is sensitive to the injection of additional carriers and the choice of electrodes is discussed. The experimental method provides the first definite evidence for hole transport in CdS. The hole drift mobility Mh at room temperature has a mean value of 15 cm2/v/sec and the hole lifetime lies between 1 X 10-7 and 3 X10-7 sec. An attempt is made to explain the temperature dependence of Mh by a model involving transport in the upper two valence bands of CdS. The mobility and effective mass ratios in these bands are estimated to be 50 and 3 respectively. The presence of about 1018 cm-3 charged defects has to be assumed. The model is used to interpret some optical properties of CdS. At room temperature the electron drift mobility Me is 275 cm 2/v/sec in agreement with recent Hall mobility and other measurements. Below about 220°K the temperature dependence of Me begins to differ significantly from that of the Hall mobility and the charge transport is predominantly controlled by shallow trapping states which may be connected with non-stoichiometric defects. In the temperature range where both Me and Mh are largely controlled by lattice scattering, none of the known theories can predict the experimental curves. It is concluded, however, that nonpolar scattering by the acoustic modes must be considered to be predominant over most of this temperature range.