This paper models the following behaviour of vehicles in mixed traffic using trajectory data. New models for the longitudinal acceleration of following vehicles are developed based on vehicle type differences and their asymmetric interactions. Two new variables capture the effect of lack of lane-discipline: lateral offset and local area concentration. These variables not only affect the follower's acceleration but also the spacing and relative speed. The following behaviour also varies across gap-narrowing and gap-widening regimes. The proposed models considerably improve the goodness-of-fit measures compared to the base models. Such models are believed to add value to microscopic simulation models of mixed traffic by enhancing their realism. © International Research Publication House.