Experiments by Maerker et al.(1) in 1998 showed that the conversion of the dilithium adduct of diphenyl acetylene, (Z)-2, to its trans derivative (E)-5 occurred at a rate that was independent of time, leading them to propose a model for this reaction. We present a detailed numerical example to illustrate that this model predicts a reaction that proceeds nearly linearly with time almost from the start to the end of the conversion. We then introduce an enhanced stationary state approximation (ESSA), with a network representation, to get accurate analytical solutions for the, time-dependent reagent concentrations predicted by this model, along with estimates of the accuracy of the solutions. Unlike the usual stationary state approximation (SSA), this ESSA allows for analytical solution during the initial transient induction period as well as the main phase of the reaction. Examinations of the network and of the analytical solutions provide an explanation for the mechanism by which this model maintains nearly zero-order kinetics throughout the reaction. This mechanism is more general than the particular reagents described here; it requires only the reaction scheme which satisfies certain inequalities. The analytical solutions show also that the conversion rate is determined mainly by the total concentration of monolithiated compounds present (a total which remains constant throughout the reactions), and the rate constant for cis-to-trans conversion of these monolithiated compounds.