Abstract: Several methods are disclosed for application in a vehicle comprising an engine, an electrical machine coupled to provide supplemental torque to a torque provided by the engine, a transmission having an input coupled to receive torque provided by the engine, and at least one wheel shaft driven by an output of the transmission, the wheel shaft having a driven end and an end coupled to a respective wheel of the motor vehicle. In one embodiment, a method for suppressing driveline oscillations comprises: for at least one wheel shaft, sensing a difference in rotational speed between the driven end of the wheel shaft and the wheel shaft's respective wheel, and generating a torque command for the electrical machine to supply a torque which is a function of the difference.