The use of hybrid electric vehicles is an effective means of reducing pollution and improving fuel economy. Certain vehicle control strategies commonly automatically shut down or restart the internal combustion engines of hybrid vehicles to improve their fuel consumption. Such an engine autostart/stop is not engaged or controlled by the driver. Drivers often do not expect or prepare for noticeable vibrations, noise, or an unsmooth transition when the engine is autostarted/stopped. Unsmooth engine autostart/stop transitions can cause driveline vibrations, making the ride uncomfortable and the customer dissatisfied with the vehicle. This research simulates the dynamic behaviors associated with the neutral starting and stopping of a power-split hybrid vehicle. The seat track vibration results of analysis and hardware tests of the baseline control strategy are correlated. Several antivibration control strategies are studied. The results reveal that pulse cancellation and the use of a damper bypass clutch can effectively reduce the fluctuation of the engine block reaction torque and the vibration of the seat track by more than 70% during the autostarting and stopping of the engine. The initial crank angle can have an effect on the seat track vibration as well.