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Vehicular powertrains with an internal combustion engine, an electronic throttle valve, and a continuously variable transmission (CVT) offer much freedom in controlling the engine speed and torque. This can be used to improve fuel economy by operating the engine in fuel-optimal operating points. The main drawbacks of this approach are the low driveability and, possibly, an inverse response of the vehicle acceleration after a kick-down of the drive pedal. This paper analyzes a concept for a novel powertrain with an additional flywheel. The flywheel plays a part only in transient situations by (partly) compensating the engine inertia, making it possible to optimize fuel economy in stationary situations without loosing driveability in transients. Two control strategies are discussed. The first one focuses on the engine and combines feedback linearization with proportional control of the CVT ratio. The CVT controller has to be combined with an engine torque controller. Three possibilities for this controller are discussed. In the second strategy, focusing on control of the vehicle speed, a bifurcation occurs whenever a downshift of the CVT to the minimum ratio is demanded. Some methods to overcome this problem are introduced. All controllers are designed, using a simple model of the powertrain. They have been evaluated by simulations with an advanced model.