Abstract: The invention provides a strategy to stop a parallel HEV powertrain engine while maintaining smooth vehicle response to driver demand using the motor while simultaneously opening an engine disconnect clutch. In the preferred embodiment, the strategy stops an engine (based on, for example, driver demand), disconnects the disconnect clutch to the powertrain, halts fuel to the engine, and predicts a desired motor/generator speed. The prediction of desired motor/generator speed can be: a trajectory comparison based on present and past vehicle velocity and deceleration or on a vehicle accelerator position, or a determination of whether the vehicle is in speed following control mode. The system can also add additional strategies such as accelerate the strategy if a vehicle brake is applied. The gradual takeover by the motor occurs by proportionally decreasing actual engine torque until engine torque is zero while maintaining vehicle velocity using for example a proportional plus integral controller.