Reducing the number of accidents that are caused by drowsiness or fatigue could be achieved by applying different strategies. This paper focuses on the on-line, real time detection of deteriorating driver state and driving behaviour, and on the question what should be done after this has been detected. It reports three studies performed in the TNO driving simulator. The first one leads to the conclusion that an in-vehicle monitoring device is best based on measures of steering activity, to which the registration of not keeping to one's lane boundary could be added. The second study points to the importance of certain personality attributes that determine who is a drowsiness-prone driver. The third study demonstrates that an alertness maintenance device (gamebox) can have positive effects on the onset of drowsiness and on the occurrence of critical events that it may cause. Altogether, the results lead to a positive conclusion with respect to the possibility of implementing of a strategy that focuses on the on-line detection of drowsiness and its consequences. Behavioural adaptation from the side of the relevant drivers to this strategy, however, is an issue of concern that needs further investigation.