A control device for an internal combustion engine (E) and a continuous variable transmission (35) according to the present invention is disposed in a power transmission method (P) between the internal combustion engine (E) mounted on a vehicle and driving wheels (32) and of which transmission ratio can be continuously changed at a predetermined transmission speed Vm so as to maintain the transmission ratio i suitable for engine speed .omega.e and vehicle speed Vc. In addition, the device controls power of the internal combustion engine (E).The control device for an internal combustion engine (E) and a continuous variable transmission (35) sets the transmission speed Vm according to a deviation .DELTA.i between an objective transmission ratio io and an actual transmission ratio in to control the continuous variable transmission (35) at the transmission speed Vm. On the other hand, it controls the power of the internal combustion engine (E) by means of transmission auxiliary torque .DELTA.Te with respect to the transmission speed Vm, so that it is possible to change the continuous variable transmission 35 at suitable transmission speed Vm. This results in reduction of the slip and shock caused on transmission operation of the continuous variable transmission (35).