To prevent an excessive load in a transmission clutch, and to prevent a problem wherein centrifugal oil pressure is generated in the transmission clutch to make a transmission torque get unstable, when slip-engaging the transmission side clutch under a travel in an electric vehicle travelling (EV travel) mode to start an engine, in a one-motor and two-clutch type of hybrid drive unit drive-connected in series with the engine of an internal combustion engine, an engine side clutch, a motor/generator, the transmission side clutch and a transmission, in this order.

When starting the engine 3, a tightening capacity of the transmission side clutch 9 is controlled to transmit a torque necessary for the travel (step S2), a tightening capacity of the engine side clutch 8 is controlled to transmit a torque necessary for the start of the engine from the motor/generator 7 to the engine 3 (step S8), and a release command is output to the engine side clutch 8 to make an initial explosion torque maximum, in self-standing of the engine (step S8).

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