SUMMARY The problems resulting from the accumulation of nitrogen and phosphorus from discharges of wastewater to sea, rivers and lakes have increased researches about new technologies and methods for wastewater treatment, mainly based on biological processes. Biological processes taking place in a WWTP consist of biochemical transformations carried out by microorganisms during their growth. Mathematical modeling of bacterial growth processes responsible for the wastewater treatment is essential for WWTP design, simulation and optimal control. Traditionally, the nitrification process, carried out by two groups of bacteria, was modeled as a single-stage process in which the ammonium was oxidized to nitrate. However, the development of new technologies and the emergence of problems caused by the accumulation of nitrite in some WWTPs make necessary to consider the nitrite as a new component in biological models. This fact led to the development of several models that considers the nitrification as a two-stage process: firstly, ammonia is oxidized to nitrite and subsequently nitrite is oxidized to nitrate. Modeling nitrification process considering nitrite as a model component involves also the modification of other processes like the growth of heterotrophic bacteria using nitrite instead of nitrate as electron acceptor. Although there are several models in the literature that considers the nitrification as a two-stage process, not yet there is a model considering nitrite as a model component, widely accepted by the scientific community. There is not a general model appropriate to address the above mentioned issues and to provide a range of parameter values to reproduce adequately reliable transformations of nitrite in activated sludge systems. In addition, there is not a defined calibration methodology for these models to determine the values of the parameters included in these models. Therefore, the main objectives of this thesis are to develop a general model of nitrification process that considers both the oxidation of ammonium to nitrite and the oxidation of nitrite to nitrate, and to develop the calibration methodology for the parameters of the bacteria involved. Aimed at validating the model in two operation systems with completely different characteristics (a laboratory scale SHARON reactor and activated sludge pilot plant) two calibration methodologies have been developed. As the evaluated systems were different these methodologies were different too. The calibration methodology of the SHARON reactor includes only the determination of the parameters values for ammonia-oxidizing bacteria (AOB) because these bacteria are the only ones present in this reactor. By contrast, in the activated sludge from the pilot plant both ammonia-oxidizing bacteria and nitrite-oxidizing bacteria (NOB) are present. The calibration methodology includes the determination of the parameters of each group of bacteria. The calibration methodologies are mainly based on respirometric batch experiments performed in the laboratory and the individual study of the different processes involved. These methodologies have been developed with a special emphasis on simplicity. They can be applied as often as necessary as they do not need a specific laboratory equipment or particularly complex laboratory techniques. The developed calibration methodologies have been applied in each of the aforementioned systems. The application of these methodologies and the FISH technique for monitoring of bacterial populations present in both systems have demonstrated that the ammonia-oxidizing bacteria present in the SHARON reactor are different from the ammonia-oxidizing bacteria present in the pilot plant. Different bacteria involved completely different values of the model parameters. The model calibration in the pilot plant has also shown the differences between ammonia-oxidizing bacteria and nitrite-oxidizing bacteria, as oxygen affinity, effect of pH, maximum growth rate,... In addition, the pilot plant was operated according to two different treatment schemes. The first one included a BABE reactor to enhance nitrification process. In the second one the BABE reactor was removed, making it possible to observe the effect of the presence of this reactor on AOB and NOB model parameters. Finally, the model has been validated in the SHARON reactor by the fit of model predictions to the experimental results obtained in these reactors. Simulations carried out using the mathematical model with the obtained parameters reproduce accurately the experimental results of these reactors.