An extended-range electric vehicle includes drive wheels, an engine having an output shaft, a planetary gear set having a node driven by the output shaft of the engine when the engine is on, and first and second electric machines. The first electric machine is connected to another node, and operates as a generator when the engine is on. A one-way clutch is connected to the remaining node. The second electric machine is connected to an output side of the one-way clutch, with a shaft connecting the drive wheels to the second electric machine. A controller provides a forward electric-only (EV) mode, a reverse EV mode, power-split mode(s), and series mode(s). The series mode(s) provide a direct mechanical path between the engine and drive wheels, with the one-way clutch overrunning in the forward EV mode. The one-way clutch may be activated passively or by a PRNDL device.