1. The patch-clamp technique was used to study channel gating kinetics of the acetylcholine receptor. The agonist carbachol was used at concentrations varying from 0.10 to 20 microM. 2. Data in which many channels were often open at the same time were analysed with the aid of mathematical expressions that relate the stochastic behaviour of a many-channel system to the kinetic parameters of a single channel. These methods provide consistent estimates of parameters. This consistency suggests that there is no correlation between the kinetics of channel closure and the density of channels in a patch of membrane. 3. Closed times were well fitted by a sum of two exponentials. Addition of a third exponential component never significantly improved the quality of the fit. 4. A sum of two exponentials usually provided the best fit to open times. The ratio of the fractions of slowly closing and rapidly closing channels increased linearly with agonist concentration, in a manner consistent with the opening of singly and doubly liganded receptor channels. 5. Analysis of closed-time densities at various times after seal formation was used to follow the time course of desensitization. No changes in the kinetics of closure were detected during desensitization. 6. At 0.10 microM-carbachol the frequency at which openings were observed was only slightly more than the background frequency of spontaneous opening. At 20 microM-carbachol, immediately after seal formation and before the onset of desensitization, the frequency of opening was approximately 300 times higher. 7. The frequency of appearance of brief-duration openings increased linearly with carbachol concentration and saturated at approximately 5 microM. The frequency of appearance of long-duration openings increased as the square of the agonist concentration, with only a slight hint of saturation. 8. The results presented here are discussed within the framework of a two-binding-site model for the allosteric activation of the acetylcholine receptor. Estimates are made of all of the equilibrium constants and many of the rate constants of the relevant reaction scheme. The two ligand binding sites are found to be very different in terms of their dissociation constants and their influence on the channel gating transitions. These results have implications for the energetics of receptor activation and for the utilization of binding energy by the receptor.