During this study, a mathematical model simulating Piggery Wastewater Treatment (PiWaT1) was developed, aiming at process optimisation. For this purpose, the effects of the temperature and the free ammonia concentration on the nitrification rates were studied using respirometry. The maximum growth rates experimentally obtained were higher for ammonium oxidizing biomass than for nitrite oxidizing biomass for the temperatures above 20°C and were equal to 1.9 and 1.35 day-1 at 35°C, respectively. No inhibition of the free ammonia concentration on the nitrification rate was observed up to 50 mgN/l. From these data and others experimental data obtained using a pilot-scale reactor, treating piggery wastewater, a modified version of ASM1 was developed and calibrated. In order to model the nitrite accumulation experimentally observed, the ASM1 was extended with two-step nitrification and denitrification including nitrite as intermediate. Finally, the PiWaT1 model allowed a good fitting with experimental data. In addition to the temperature, the oxygen concentration was also identified as an important factor influencing the nitrite accumulation during nitrification. Even if some improvements of the model are always necessary, this model could be used for process improvement.