•A diving simulator was used to study overtaking of cyclists with oncoming traffic.•The TTC between subject and oncoming vehicle affected drivers’ overtaking strategy.•The TTC between subject and oncoming vehicle influenced safety margins to cyclists.•Safer margins of 0.93 m were found for drivers not waiting for oncoming traffic.•Different speeds were adopted by drivers depending on the overtaking strategy. Active transportation - such as cycling - can provide health benefits to the population. However, cycling safety remains a major threat to favour the use of bicycles and, for this reason, more efforts are needed to reduce the number of crashes involving cyclists. One crash scenario which deserves special attention is driver’s overtaking of cyclists since it has an increased likelihood to lead to severe injuries. During the overtaking manoeuvre, the monitoring of subjective risk can influence the decision-making process and lead to different outcomes. In this context, the present driving simulator study aims to investigate how the time to collision between oncoming traffic and subject vehicle affected the overtaking strategy, and the minimum safety margins towards the overtaken cyclist. The results show that a decrease in time to collision against the oncoming vehicle significantly affects the drivers’ overtaking strategy (accelerative vs. flying), inducing more drivers to choose an accelerative overtaking manoeuvre. The decrease in time to collision also produces a decrease in minimum safety margins to the cyclists for drivers who opt for a flying overtaking strategy. Finally, the current research shows that the minimum lateral safety margins were smaller and the mean speed higher in flying manoeuvres compared to accelerative manoeuvres. Overall, the combination of lower safety margins and higher mean speeds in flying overtaking manoeuvres seems to pose a risk for cyclists’ safety. The findings of the study provide some implications for the design of automated driving.