The interaction of the anticholinesterase organophosphorus compounds with acetylcholinesterase has been regularly characterized as a straightforward phosphylation of the active site serine (Ser-203) which can be described kinetically by the rate inhibitory rate constant ki. However, more recently certain kinetic complexities in the inhibition of acetylcholinesterase by organophosphates such as paraoxon (O, O-diethyl O-(p-nitrophenyl) phosphate) have raised questions regarding the adequacy of the kinetic scheme on which ki is based. The present report documents conditions in which the inhibitory capacity of paraoxon towards human recombinant acetylcholinesterase appears to change as a function of oxon concentration (as evidenced by a changing ki), with the inhibitory capacity of individual oxon molecules increasing at lower oxon concentrations. Computer models for the inhibition of acetylcholinesterase based on the ki scheme, as well as an Ordered Uni Bi reaction scheme from which the ki scheme was derived, were unable to accurately simulate inhibition by paraoxon at both high (100 nM) and low (78 pM) concentrations without allowing for changes in the values of certain kinetic parameters. For example, with the Ordered Uni Bi reaction scheme, adjusting the binding constants and/or the phosphorylation constant in a concentration-dependent manner resulted in accurate simulations of the inhibition of acetylcholinesterase over a wide range of paraoxon concentrations. Conversely, alterations in the reactivation of phosphorylated enzyme had little effect on the simulated inhibition profiles. (Supported in part by grant ES012648 from NIEHS).