In a vehicle dynamics control apparatus capable of balancing a vehicle dynamics stability control system and a lane deviation prevention control system, a cooperative control section is provided to make a cooperative control between lane deviation prevention control (LDP) and vehicle dynamics stability control (VDC). When a direction of yawing motion created by LDP control is opposite to a direction of yawing motion created by VDC control, the cooperative control section puts a higher priority on VDC control rather than LDP control. Conversely when the direction of yawing motion created by LDP control is identical to the direction of yawing motion created by VDC control, a higher one of the LDP desired yaw moment and the VDC desired yaw moment is selected as a final desired yaw moment, to prevent over-control, while keeping the effects obtained by both of VDC control and LDP control.