A drive system including first and second power sources, first and second output shafts, a differential mechanism, and an electronic control unit, and a control method therefor are provided. The differential mechanism is configured such that the second power source is connected to a first rotating element, one output shaft of a vehicle is connected to a second rotating element, and the other output shaft of the vehicle is connected to a third rotating element so as to be able to be connected to or disconnected from the third rotating element by a connect-disconnect mechanism, and includes at least one of an engagement element that selectively engages any two of the three rotating elements and an engagement element that selectively engages the third rotating element to a fixing member. The electronic control unit is configured to, during turning, prohibit switching between a first drive mode and a second drive mode.