Abstract: In an automatic transmission gear system which selectively actuates a plurality of frictional elements by oil pressure such as clutches and brakes that are provided in the transmission gear system in order to obtain different gear ratios, one frictional element is disengaged concurrently with engaging of another frictional element for switching the gear ratio (speed change). At that time, it is important to adjust the timing for actuating the frictional elements depending on the conditions of the engine and the vehicle itself. The present invention relates to a control device for an automatic transmission gear system which assures smooth gear shifting at all times by adequately controlling the overlap of the torque capacities of the frictional elements.