The performance of an upflow packed-bed biofilm reactor has been analyzed under dual substrate limitation conditions. The numerical solution of the proposed equations defining the system has been obtained for a wide range of operating conditions for a case of practical significance involving glucose and oxygen as dual substrates. The results show that the inlet glucose concentration defines the limiting substrate at a position near the inlet of the reactor. For inlet glucose concentrations up to 300 mg/l, glucose acts as the limiting substrate. However, for inlet concentrations of 400 mg/l of glucose or higher, oxygen assumes the role of the limiting substrate at that position. For all other positions in the reactor, glucose acts as the limiting substrate, irrespective of its inlet concentration. Extensive computations were performed in order to define regions where glucose, oxygen or both are limiting. The predicted results have been found to be in agreement with the theoretical criteria, proposed in the literature, of determining the limiting substrate.