A mathematical model was developed to describe the dynamic behaviour of the anaerobic mesophilic digestion. Special emphasis was given to the acetate degradation kinetics, as the step that determines the stability of anaerobic digestion. From the safety factor (maximum/average degradation rate) of acetate degradation in the range of 5.3 to 23 days hydraulic detention time, a maximum observed growth rate of 0.37 d−1 and decay rate of 0.10 d−1 were estimated. Temperature and pH dependence of acetate conversion was also determined and included in the model. The model was verified with load variation experiments on laboratory and full scale digesters. Mesophilic digestion with anaerobic thermophilic pretreatment is more sensitive to load variation than single mesophilic digestion. However two stage treatment leads to better sludge characteristics (thickening, viscosity, COD, TSS) of the treated sludge.