At high and medium magnetic field, the transverse NMR relaxation rate (T-1(2)) of water proteins in blood is determined predominantly by the oxygenation state of haemoglobin. T-1(2) depends quadratically on the field strength and on the proportion of haemoglobin that is deoxygenated. Deoxygenation increases the volume magnetic susceptibility within the erythrocytes and thus creates local field gradients around these cells. From volume susceptibility measurements and the dependence of T-1(2) on the pulse rate in the Carr-Purcell-Meiboom-Gill experiment, we show that the increase in T-1(2) with increasing blood deoxygenation arises from diffusion of water through these field gradients.