Endothelium-dependent hyperpolarization of vascular smooth muscle is a mechanism that contributes to the vasodilator response to shear stress and chemicals acting on endothelial receptors. The phenomenon is explained by the release from endothelial cells, of an endothelium-derived hyperpolarizing factor(s) (EDHF) (s), although its (their) exact nature is still controversial. Indeed, endothelial cells produce several substances that are capable of evoking hyperpolarization in vascular smooth muscle. However, which of these factors represents EDHF under physiological conditions remains unknown. The term EDHF should be reserved for a substance(s) that differs from both NO and prostaglandins. In this review Jean-Vivien Mombouli and Paul M. Vanhoutte consider the possible candidates for EDHF and the arguments that have lead to the proposal that these substances fulfil the functions of an endothelium-derived relaxing agent. The weaknesses of the available sudies are also discussed. The identification of EDHF would allow the understanding of its physiological role alongside other known endothelial mediators such as NO and prostacyclin. This could lead to the design of new therapies aimed at correcting the impairment of EDHF-mediated dilatation in a number of cardiovascular diseases.