Abstract The Reinforcement Sensitivity Theory of Personality has as its main foundation a Behavioural Inhibition System (BIS), defined by anxiolytic drugs, in which high trait sensitivity should lead to internalising, anxiety, disorders. Conversely, it has been suggested that low BIS sensitivity would be a characteristic of externalising disorders. BIS output should lead to increased arousal and attention as well as behavioural inhibition. Here, therefore, we tested whether an externalising disorder, Attention Deficit Hyperactivity Disorder (ADHD), involves low BIS sensitivity. Goal-Conflict-Specific Rhythmicity (GCSR) in an auditory Stop Signal Task is a right frontal EEG biomarker of BIS function. We assessed children diagnosed with ADHD-I (inattentive) or ADHD-C (combined) and healthy control groups for GCSR in: a) an initial smaller study in Dunedin, New Zealand (population ~120,000: 15 control, 10 ADHD-I, 10 ADHD-C); and b) a main larger one in Tehran, Iran (population ~9 [city]-16 [metropolis] million: 27 control, 18 ADHD-I, 21 ADHD-C). GCSR was clear in controls (particularly at 6–7 Hz) and in ADHD-C (particularly at 8–9 Hz) but was reduced in ADHD-I. Reduced attention and arousal in ADHD-I could be due, in part, to BIS dysfunction. However, hyperactivity and impulsivity in ADHD-C are unlikely to reflect reduced BIS activity. Increased GCSR frequency in ADHD-C may be due to increased input to the BIS. BIS dysfunction may contribute to some aspects of ADHD (and potentially other externalising disorders) and to some differences between the ADHD subtypes but other prefrontal systems (and, e.g. dopamine) are also important.