In this paper, in order to study non-lane-based car-following, the non-coaxiality concept is defined, where there is a significant lateral difference between the leader and follower vehicle. Two main reasons for non-coaxiality were addressed by drivers in the interview: providing more visible distances beyond leader vehicle and increasing the possibility of escaping in sudden brakes to avoid rear-end collision. Results showed that non-lane-based behavior was due to the effect of the existence of other cars in the traffic flow. By reducing speed or increasing density, vehicles more affect each other. But this trend will continue up until vehicles fill the free spaces. In other words, vehicles make others stick to the leader’s path in high-density flow. Studying the relationship between lateral distance and time headway demonstrated that time headway threshold for initiation of car-following behavior in Iranian drivers can be approximately 2 seconds. In this study, Overtaking was defined as a part or continuation of the non-lane-based driving behavior. For overtaking on the left, steering angle, the final lateral distance and the lateral speed difference between the follower and leader were 33%, 28% and 15% less than overtaking on the right.