Anaerobic digestion has been investigated as a potential method for treating antibiotic contaminated livestock wastewaters. Antibiotic removal is mainly associated with biodegradation and sludge adsorption. In environmental concentrations, i.e., from ng L-1 to a few hundred lig L-1, cometabolism is the most likely biodegradation pathway. The overall performance of anaerobic processes may be affected by the hydraulic retention time, and these processes are strongly related to the physical characteristics of the reactor and variations in influent chemical composition. The effects of these factors can be better understood using a mathematical model. Therefore, this paper aimed to develop a model to describe an anaerobic process to treat sulfamethazine (SMZ), which was divided into two stages of microorganism growth and substrate consumption. In addition, three hypotheses regarding sulfamethazine degradation, including substrate cometabolism related to both stages and an apparent enzymatic reaction, were evaluated. A long-term kinetics structure was added to the model to simulate the process of adaptation to each new operational condition. The results showed that sudden increases in chemical oxygen demand (COD) and hydraulic retention time (HRT) had the most significant negative impact on process performance. In addition, a sudden variation of 8 mu g of SMZ had a similar impact on the process as did 1000 mg of filtered COD. Of the degradation hypotheses, the hypothesis related to organic acid consumption was more accurate than that related to hydrolysis; however, neither could account for the response to variations in HRT. The enzymatic approach resulted in a considerably more accurate representation of the influent flow rate variations than did the cometabolic hypotheses. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.