Endothelium-derived hyperpolarizing factor is defined as that substance which produces vascular smooth muscle hyperpolarization which cannot be explained by nitric oxide or by a cyclo-oxygenase product such as prostacyclin. The possibility that the factor is an epoxyeicosatrienoic acid or a cannabinoid agonist such as anandamide continues to be investigated, but definitive evidence in favour of either is lacking. The sensitivity of EDHF-mediated responses to charybdotoxin, to apamin or to mixtures of these two toxins may indicate the opening of more than one smooth muscle K-channel, but the possibility that these are located on the vascular endothelium is discussed.