This work established a mathematical model that formulated degrader formation by conversion of indigenous microbial cells. Degrader conversion is attributed to genetic induction whose force is dependent on the strength of acclimating xenobiotic and the amount of indigenous cells. After successful conversion, which requires an amount of time proportionate to the lag, degraders grow on the xenobiotic substrate. This model formulated the lag and degrader formation with the sigmoid function and degrader growth with the Haldane kinetics. The model so completed accurately simulates the degradation and biomass courses during acclimation and degradation of a xenobiotic by indigenous activated sludge, wherein the factors relating to the acclimation process are given values. The model serves the need for a rational representation of microbial acclimation to a xenobiotic. (C) 2009 Elsevier Ltd. All rights reserved.