A systematic survey of the acetylcholine-mimetic 2,4-dioxa-3-phosphadecalins as irreversible inhibitors of acetylcholinesterase revealed hitherto overlooked properties as far as the kinetic mechanisms of interaction are concerned. As a support to past and future work in this field, we describe the kinetics of eight reaction schemes that may be found in irreversible enzyme modification and compare them with two mechanism of reversible, slow-binding inhibition. The relevant kinetic equations and their associated graphical representations are given for all mechanisms, and concrete examples illustrate their practical use. Since irreversible inhibition is a time-dependent phenomenon, kinetic analysis is greatly facilitated by fitting the appropriate integrated rate equations to reaction-progress curves by nonlinear regression. This primary scrutiny provides kinetic parameters that are indispensable tools for diagnosing the kinetic mechanism and for calculating inhibition constants. Numerical integration of sets of differential equations is an additional useful investigation tool in critical situations, e.g., when inhibitors are unstable and/or act as irreversible modifiers only temporarily.