To increase an amount of torque transmitting of a deceleration drive device, and to reduce shock of engagement.

The deceleration drive device has a transmission motor 5 capable of outputting torque, first and second deceleration mechanisms 33, 35 for decelerating torque of the transmission motor 5, and a rear differential gear 37 for distributing output of the first and second deceleration mechanisms 33, 35 to axles 25, 27 side. An engaging clutch 91 capable of operating for switching the output of the second deceleration mechanism 35 to the rear differential gear 37 between transmission and interruption is provided. When the engaging clutch 91 operates for transmission of the output after start of the output of the transmission motor 5, a regulating means 93 for regulating engagement connection of the engaging clutch is provided until output side rotation speed of the second deceleration mechanism 35 and input side rotation speed of the rear differential gear 37 correspond so as to be suitable for engagement.