Abstract: There is disclosed a speed control apparatus installed in an automobile equipped with an automatic transmission. This apparatus includes a microcomputer, an input interface circuit, an output interface circuit, an actuator for the automatic transmission, and an actuator for maintaining the speed of the automobile at the speed set by the driver. The apparatus controls the operation of the transmission in such a way that it shifts into another gear, depending on the automobile speed or engine speed and also on the engine load or the throttle opening. The speed set by the driver is maintained by controlling the throttle opening. The apparatus estimates the driving force of the transmission when it makes an upshift, from the present speed, the present throttle opening, and the present transmission gear. If the estimated force is not sufficiently large, then such an upshift is inhibited.