The performance of an upflow packed-bed biofilm reactor was investigated by considering simultaneous methanogenesis and denitrification reactions under step and sinusoidal variations of feed concentration and temperature. For simultaneous step inputs of 20 mg dm(-3) of NO3--N and 60 mg dm(-3) of methanol, the proposed model shows that major conversion of both the substrates takes place in the first half of the reactor. However, when the inlet concentration of methanol is subjected to sinusoidal variation, while that of NO3--N is maintained stepwise, the exit concentration of both methanol and NO3--N follow a sinusoidal response. On the other hand, when the inputs are reversed (methanol stepwise and NO3--N sinusoidal), the response exhibits similar behaviour. For sinusoidal variation of feed temperature the exit concentration profiles of both substrates also follow a sinusoidal pattern. For methanol, the mean steady state conversion under sinusoidal variation is higher than the corresponding steady state concentration when feed temperature is constant at 30 degrees C. The model predictions are in good agreement with the experimental data available in the literature.