The definition, formulation, and importance of vehicle 'critical speed' have been well documented in the vehicle dynamics literature. One of the main current research directions in vehicle dynamics and control is to enhance the understanding of characteristics of driver-vehicle systems. However, no efforts have been attempted in the literature to derive a new mathematical formulation for the 'critical speed' in the context of driver-vehicle systems, in order to capture the contributions of human driver properties, apart from the vehicle properties. This study derives two alternative analytical formulations for the 'critical speed' in driver-vehicle systems using two different simplified driver-vehicle system models. These two new formulations for the 'critical speed' are a function of vehicle/tire parameters as well as human driver model parameters, such as driver preview time, delay time, and control gain. Simulation analyses are then conducted to evaluate and demonstrate the effectiveness of the derived 'critical speed' formulations, compared with the results from a relatively more comprehensive driver-vehicle system model. It is further demonstrated that one of the formulations derived could also be able to predict the system instability or 'critical speed' for neutral-or under-steered vehicles, in driver-vehicle systems, apart from that for over-steered vehicles.