The investigation aimed to present mathematical models for describing the dynamic behavior of the dissolved organic matter removal and nitrification in the Aerated Submerged Bio-Film (ASBF) for a plug-flow reactor. Based on the experimental data from the batch system of the ASBF pilot plant, mathematical models for the plug-flow reactor were developed to predict dissolved organic matter and ammonia nitrogen removal rates as a function of heterotrophic and autotrophic bacteria populations, dissolved organic matter concentrations, ammonia nitrogen concentrations, dissolved oxygen concentrations, and temperature. The mathematical models for dissolved organic matter and ammonia nitrogen removal in ASBF include two differential equations reflecting heterotrophic and autotrophic bacteria populations, and a number of kinetic parameters. Consequently, the results present a better insight into the dynamics behavior of heterotrophic and autotrophic biofilm growth and their practical application to wastewater for dissolved organic matter and ammonia nitrogen removal process. The mathematical model for ammonia nitrogen and dissolved organic matter removals present good results for the plug-flow reactor.