Insulin and insulin-like growth factor-I exhibit a set of non-classical receptor binding properties suggestive of negative co-operativity or site-site interactions between the two receptor halves: curvilinear Scatchard plots, acceleration of dissociation of bound labelled ligand at high dilution in the presence of unlabelled ligand. The alpha 2 beta 2 receptor dimer binds only one ligand molecule with high affinity. The dose-response curve for the acceleration of 125I-insulin by unlabelled insulin is bell-shaped, with a disappearance of the negative co-operativity at insulin concentrations over 0.1 mumol/l. This phenomenon had been attributed to insulin dimerization, but new data with non-dimerizing analogues and insulins modified at the hexamer-forming surface indicate the presence of a second binding site on the insulin molecule's hexamer face. This site binds to a second domain on the receptor. A new binding model for insulin and insulin-like growth factor-I is proposed where the bivalent ligand bridges the two receptor alpha subunits alternatively at opposite sites in a symmetrical receptor structure. The implications of the model for negative co-operativity, bell-shaped biological curves, and the divergence between mitogenic and metabolic signalling are discussed in the context of the evolution of the properties of insulin and insulin-like growth factor-I.