The muscarinic acetylcholine receptor antagonists, atropine and pirenzepine, produced an apparent insurmountable antagonism of muscarinic M₁ receptor-mediated intracellular Ca²⁺ mobilization in Chinese hamster ovary (CHO) cells when tested against the agonists carbachol or xanomeline. Each antagonist caused a dextral shift of the agonist concentration–response curves with depression of the maximum response that was incomplete (i.e., saturated) and which varied with the pairs of agonist and antagonist. Equilibrium competition binding assays found no deviation from simple, reversible competitive behavior for either antagonist. The relative rates of dissociation of unlabeled atropine and pirenzepine were also assessed in radioligand kinetic studies and it was found that atropine dissociated from the receptor approximately 8-fold slower than pirenzepine. Numerical dynamic simulations suggested that the insurmountability of antagonism observed in the present study was probably a kinetic artifact related to the measurement of transient responses to a non-equilibrated agonist in the presence of a slowly dissociating antagonist. Importantly, the patterns of antagonism observed included a saturable depression of agonist maximal response, a mode of antagonism that is incompatible with the previously described phenomenon of hemi-equilibrium states. Monte Carlo simulations indicated that reasonable, semi-quantitative estimates of antagonist potency could be determined by a minor modification of standard methods, where equieffective agonist concentrations, rather than EC₅₀ values, are compared in the absence and presence of antagonist. Application of the latter approach to the functional data yielded estimates of antagonist potency that were in excellent agreement with those derived from the equilibrium binding assays, thus indicating that the present method can be useful for quantifying antagonist potency under non-equilibrium conditions.