At the start of the 21st century overtaking on two-lane rural roads is a major traffic safety problem. However, this dissertation research demonstrates that most drivers are perfectly able to safely perform these manoeuvres. Their time spent in the left lane is about eight seconds. Preparing subtasks of the manoeuvre, such as checking surrounding vehicles' behaviours, changing gear and starting accelerations are started in the right lane. In this way, available overtaking gap in the oncoming traffic stream are optimally used. This anticipative behaviour is accounted for in the proposed overtaking assistant design, which informs the driver about overtaking gaps three seconds before they become available. This system is developed to assist less daring drivers with overtaking and to prevent risk-taking drivers to perform overtaking manoeuvres in unsafe situations. A driving simulator experiment demonstrated that this assistant does not much affect overtaking efficiency, drivers' comfort or safety, as long as the threshold for a safe gap is chosen such that the safety margin with the first oncoming vehicle remains above three seconds. A microscopic traffic simulation study shows that when this threshold is eleven seconds, traffic system efficiency remains similar or increases slightly due to increased number of overtaking manoeuvres. Drivers' safety during overtaking increases, because the time-to-collision with oncoming vehicles will not become smaller than three seconds. And, drivers' comfort is improved in terms of higher overtaking frequencies and less time spent following. To introduce the proposed overtaking assistant to the market, vehicle-to-vehicle communication is necessary. This technology enables vehicles to localise all other surrounding vehicles. The automotive industry works hard on the development of vehicle-to-vehicle communication, however, it will take at least another ten years before the first overtaking assistant as proposed in this dissertation, will become available.