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In this article, two models are developed for the adhesion force in railway rolling stocks. The first model is a static model based on a beam model, which is typically used to model automobile tires. The second model is a dynamic model based on a bristle model, in which the friction interface between the rail and the wheel is modeled as contact between bristles. The validity of the beam model and bristle model is verified through an adhesion test using a brake performance test rig. We also develop wheel-slip brake control systems based on each friction model. One control system is a conventional proportional-integral (PI) control scheme, while the other is an adaptive sliding mode control (ASMC) scheme. The controller design process considers system uncertainties such as the traveling resistance, disturbance torque, and variation of the adhesion force according to the slip ratio and rail conditions. The mass of the rolling stocks is also considered as an uncertain parameter, and the adaptive law is based on Lyapunov stability theory. The performance and robustness of the PI and adaptive sliding mode wheel-slip brake control systems are evaluated through computer simulation.