Nuclear‐magnetic‐resonance spin‐lattice relaxation measurements were conducted in a Bentheimer sandstone sample for drainage experiments involving gas‐liquid fluid phases with ten different saturation levels ranging from complete water saturation (Sw=1) down toSw=0.14. A monotonic decrease in relaxation times was observed as the water saturation was lowered over this broad saturation range. This phenomenon is explained by considering that for a drainage process the liquid (wetting) phase was drained from different‐sized pores at different saturations with larger pores being drained first. The relaxation decay curves corresponding to each saturation state were analyzed using both stretched exponential and discrete multiexponential functions. In particular, the effect due to bulk fluid relaxation was eliminated so that a more appropriate relationship between pore size distribution and the relaxation rate is obtained. From these analyses, the relative variation of pore size distributions corresponding to different saturation levels was obtained. A power‐law dependence of saturation with relaxation times is observed which indicates that the relaxation analysis can be used to characterize fluid saturations.