Vehicular powertrains with an internalcombustion engine, an electronic throttle valve anda continuously variable transmission (CVT) offermuch freedom in controlling the engine speed andtorque. This can be used to improve fuel economyby operating the engine in fuel optimal operatingpoints. The main drawbacks of this approach arethe low driveability and, possibly, an inverse responseof the vehicle acceleration after a kick-down of thedrive pedal. This paper analyzes a concept for a novelpowertrain with an additional flywheel. The flywheelplays a part only in transient situations by (partly)compensating the engine inertia, making it possibleto optimize fuel economy in stationary situationswithout loosing driveability in transients. Two controlstrategies are discussed. The first one focuses onthe engine and combines feedback linearization withproportional control of the CVT ratio. The CVTcontroller has to be combined with an engine torquecontroller. Three possibilities for this controller arediscussed. In the second strategy, focusing on controlof the vehicle speed, a bifurcation occurs whenevera downshift of the CVT to the minimum ratio isdemanded. Some methods to overcome this problemare introduced. All controllers are designed, usinga simple model of the powertrain. They have beenevaluated by simulations with an advanced model.