Inattention and distraction account for a substantial number of traffic accidents. Therefore, we examined the impact of secondary task performance (an auditory oddball task) on a primary driving task (lane keeping). Twenty healthy participants performed two 20-min tests in the Divided Attention Steering Simulator (DASS). The visual secondary task of the DASS was replaced by an auditory oddball task to allow recording of brain activity. The driving task and the secondary (distracting) oddball task were presented in isolation and simultaneously, to assess their mutual interference. In addition to performance measures (lane keeping in the primary driving task and reaction speed in the secondary oddball task), brain activity, i.e. event-related potentials (ERPs), was recorded. Performance parameters on the driving test and the secondary oddball task did not differ between performance in isolation and simultaneous performance. However, when both tasks were performed simultaneously, reaction time variability increased in the secondary oddball task. Analysis of brain activity indicated that ERP amplitude (P3a amplitude) related to the secondary task, was significantly reduced when the task was performed simultaneously with the driving test. This study shows that when performing a simple secondary task during driving, performance of the driving task and this secondary task are both unaffected. However, analysis of brain activity shows reduced cortical processing of irrelevant, potentially distracting stimuli from the secondary task during driving.