1 The behaviour of the divalent cations Ca and Sr as agonists for receptors that mediate the synchronous evoked secretion of acetylcholine (ACh) was studied in the hope of determining whether the relationship between Ca binding and ACh secretion is determined only by the law of mass action or by the mathematical framework of receptor theory. Experiments were designed to evaluate the assumption that maximum effect requires occupation of all receptors by testing for the presence of spare Ca receptors on presynaptic terminals. Frog cutaneous nerve-muscle preparations were employed in conjunction with conventional electrophysiological methods.2 Curves of log [Ca] or log [Sr] against the mean number of ACh quanta released (m) were constructed to saturation. The log [Sr]-m relationship was shifted to the right and had a smaller maximum than the log [Ca]-m curve. This suggests that Ca has a higher efficacy than Sr and raises the possibility that spare binding sites are present for Ca.3 As a qualitative test for spare Ca receptors, La(3+) (>/=0.5 mum) or 2-chloroadenosine (25 mum) was employed as an irreversible antagonist of the effects of extracellular Ca on evoked ACh release. Despite the irreversible blockade of a proportion of receptors, increases in the [Ca] overcame this antagonism and produced a parallel shift in the log [Ca]-m relation to the right. This suggests an apparent receptor reserve for Ca. Antagonism of Sr-mediated ACh release by either La(3+) or 2-chloroadenosine could not be overcome by increasing the [Sr].4 As a quantitative test for spare Ca binding sites, the equilibrium affinity constant for Sr(K(Sr)) as a competitive inhibitor of Ca was determined and compared with values for K(Sr) calculated by two other methods which invoke the spare receptor assumption. All three methods produced comparable results. (K(Sr) = 0.24-0.27 mm(-1)).5 The equilibrium affinity constant for Ca (K(Ca)) was calculated by comparing reciprocal plots of the concentrations of Ca that produce equal levels of ACh release in the presence and absence of La(3+) (0.5 mum-3 mum). K(Ca) was estimated to be between 0.02 and 0.06 mm(-1).6 Efficacy (e), which is thought to reflect the ability of Ca or Sr once bound to receptors to support ACh release, was determined by the modified occupation theory of Stephenson (1956). The e(Ca) was estimated to be 9-20 and e(Sr) was 0.2-0.5.7 The experimentally determined values for K(Ca), K(Sr), e(Ca), e(Sr) along with the assumptions that spare Ca binding sites exist and that the non-linearities in the log [Ca] or log [Sr]-m curves are introduced beyond the sites of binding and efficacy were used to generate theoretical log [Me]-m curves. The theoretical relationships were similar to the experimental results.8 The results suggest that spare Ca receptors are present at motor nerve endings and that receptor theory provides an accurate quantitative description of the lumped events between Ca binding and ACh secretion. The possible physical correlates of affinity and efficacy are discussed.