Abstract: Automatic transmission control device with stepped gears comprising a torque converter (1) equipped with bridging means (6, 6'), a planetary gear train (2), several hydraulic receivers (E.sub.i, F.sub.i) assuring the switching of planetary gear train (2), and a hydraulic distributor (16, 17) delivering a line pressure PL, which makes it possible to feed selectively receivers (E.sub.i, F.sub.i) under the control of a computer, according to the data concerning the operation of the vehicle equipped with the transmission, characterized in that at least one switching element (8) is dimensioned to be able to slip in a controlled manner, particularly when converter (1) is bridged, in response to a momentary reduction of line pressure PL, and in that this slipping is servocontrolled, by line pressure PL, at set values depending on torque Cm and engine speed .omega.m.