In a control device for a vehicular power transmitting device, if engine torque TE generated with using a fuel other than a basic fuel by an internal combustion engine (8) connected to a shifting mechanism (10) for power transmitting capability, exceeds torque TES generated with using a basic fuel, a downshift is initiated at a lower accel-opening than that at which the downshift is initiated with using the basic fuel. That is, the shifting is performed at a shift point enabling the suppression of a torque increase in consideration of an increase in engine torque TE generated by the internal combustion engine, thereby preventing rotary elements of the shifting mechanism (10) from reaching high-speed rotations during a transition in downshift. This minimizes a drop in durability of the shifting mechanism (10).