This article presents a mathematical model of membrane-attached biofilm (MAB) behavior in a single-tube extractive membrane bioreactor (STEMB). MABs can be used for treatment of wastewaters containing VOCs, treatment of saline wastewaters, and nitrification processes. Extractive membrane bioreactors (EMBs) are employed to prevent the direct contact between a toxic volatile pollutant and the aerated gas by allowing counterdiffusion of substrates; i.e., pollutant diffuses from the tube side into the biofilm, whereas oxygen diffuses from the shell side into the biofilm. This reduces the air stripping problems usually found in conventional bioreactors. In this study, the biodegradation of a toxic VOC (1,2-dichloroethane, DCE) present in a synthetic wastewater has been investigated. An unstructured model is used to describe cell growth and cell decay in the MAB. The model has been verified by comparing model predicted trends with experimental data collected over 5 to 20-day periods, and has subsequently been used to model steady states in biofilm behavior over longer time scales. The model is capable of predicting the correct trends in system variables such as biofilm thickness, DCE flux across the membrane, carbon dioxide evolution, and suspended biomass. Steady states (constant biofilm thickness and DCE flux) are predicted, and factors that affect these steady states, i.e., cell endogeneous decay rate, and biofilm attrition, are investigated. Biofilm attrition does not have a great influence on biofilm behavior at low values of detachment coefficient close to those typically reported in the literature. Steady-state biofilm thickness is found to be an important variable; a thin biofilm results in a high DCE flux across the membrane, but with the penalty of a high loss of DCE via air stripping. The optimal biofilm thickness at steady state can be determined by trading off the decrease in air stripping (desirable) and the decrease in DCE flux (undesirable) which occur simultaneously as the thickness increases.