AbstractReaction delay is an indispensable factor in the operation and control process of drivers in a car-following scenario. Utilizing trajectory data obtained from an instrumented vehicle, this paper proposes a data-driven neural network car-following model incorporating instantaneous reaction delay of the drivers in nonlane-based (or disorderly) traffic systems. Considering instantaneous reaction delay as the time interval between relative speed and acceleration, a model is developed where the lateral descriptor of vehicle interaction (or centerline separation, CS) is found as a significant factor in modeling reaction delays in such disordered systems. Interestingly, reaction delays were found to increase with lateral separation between the interacting vehicles. Modeling results further indicate that the car-following model with instantaneous reaction delay outperformed the model with fixed reaction delay. In addition, the proposed model also showed better performance in terms of trajectory reproducing accuracy when compared with the classic car-following models. The results of this work justify the importance of considering CS in the development of algorithms for future autonomous traffic of disorderly traffic environments.