<p>The lateral dynamics of railway vehicle are affected by not only lateral force but also longitudinal force, resulting from the coupling mechanism and nonlinear saturation characteristics inherent in wheel-rail creep. This research studies the coupling mechanism of longitudinal and lateral creep under traction/braking conditions considering creep nonlinear saturation characteristics and variable friction coefficient based on Polach theory by linearizing the expression of creep force at the working point with steady tangent torque. Without loss of the generality of the analysis, various influencing factors under traction/braking conditions are normalized to creep saturation degree. Then the influence of creep saturation degree on the amplitudes of hunting motion is studied analytically through calculating the limit cycles of lateral and yaw movements of wheelset and bogie respectively, and the conclusion that the amplitudes of lateral and yaw movements will decrease with higher creep saturation degree until the system converges is drawn. The dominant frequency and Poincaré map have also been studied. Based on the analytical analysis results, a control strategy involving applying the traction and braking torque to motor vehicle and trailer respectively and reducing friction coefficient through rail lubrication is proposed to improve hunting stability. The high-speed train model with a motor vehicle and a trailer is established in SIMPACK, and the simulation results prove the effectiveness of the control strategy on vehicle’s stability on tangent tracks.</p>