This paper is concerned with whether transport accident risk tends to peak at particular times, in relation to both time of day and time on task, and with the underlying causes of such peaks. Macro-analyses confirmed the presence of a clear circadian (ca 24 hour) rhythm in road accident risk with a major peak at ca 03:00 but suggested that this rhythm could not be entirely accounted for in terms of drivers falling asleep at the wheel. Sleep propensity clearly shows a pronounced circadian rhythm and performance efficiency in wakeful subjects shows a similar trend implying that the 03:00 road accident peak may simply reflect lowered performance capabilities. However, there are 'residual' peaks in accidents at certain times of day that are difficult to account for in terms of circadian rhythmicity. It is suggested that these may reflect a time on task effect which shows a pronounced, but transient, 2-4 hour peak in risk. Only when individuals had been on duty for 12 hours or more did the risk exceed that found during the 2-4 hour peak. While an explanation for this transient peak is offered, the underlying reason for it is, as yet, uncertain and clearly warrants investigation in view of its practical implications. It is concluded that there are 'black times' when accidents are far more likely and that there is a strong need to investigate possible countermeasures.