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This paper focuses on modeling of torque-biasing devices of a four-wheel-drive system used for improving vehicle stability and handling performance. The proposed driveline system is based on nominal front-wheel-drive operation with on-demand transfer of torque to the rear. The torque biasing components of the system are an electronically controlled center coupler and a rear electronically controlled limited slip differential. Kinematic modeling of the torque biasing devices is introduced including stage transitions during the locking stage and the unlocking/slipping stage. Analytical proofs of how torque biasing could be used to influence vehicle yaw dynamics are also included in the paper. A yaw control methodology utilizing the biasing devices is proposed. Finally, co-simulation results with Matlab®/Simulink® and CarSim® show the effectiveness of the torque biasing system in achieving yaw stability control.