The methanol to olefin process on ZSM-5 was studied in an integral tubular reactor at atmospheric pressure and over a temperature range of 360-480 degreesC. Eight kinetic models based upon the elementary steps of the conversion of methanol over dimethyl ether into olefins were tested. They contained more than 30 parameters. The model parameters were transformed to include the physicochemical constraints in the parameter estimation itself, instead of accounting for these a posteriori. The estimation was performed by the genetic algorithm, followed by the Levenberg-Marquardt routine, but in combination with sequential quadratic programming to account for the constraints. The finally retained model corresponds to a mechanism that proceeds over oxonium methylide formed from a methoxy ion interacting with a basic site of the catalyst. The ylide subsequently reacts with dimethyloxonium ions to generate in parallel the primary products ethylene and propylene. Through steps of carbenium ion chemistry, the latter lead to higher olefins but also, to a lesser extent, to paraffins and aromatics.