A method of controlling a power transmission device between a driving engine and a drive axle comprising a torque converter and an automatic step gearbox, and a power transmission device for carrying out the method. In the gearbox, an electric control device with a microcomputer permits the operator to select, by means of a direction selector, the desired driving direction of the vehicle even when moving opposite to the desired direction. When such a directional command signal is sent to the control device, the reversing gear control reverses the working direction of the gearbox to make it work in the opposite direction to the driving direction. This signal is also sent to the drive gear control in the control device which during retardation maintains the engaged gear in engagement. If the highest gear is engaged when the command signal is changed, however, downshifting to the next higher gear immediately takes place which gear is then maintained during retardation. The reversing gear control is prevented from reversing the working direction of the gearbox if the vehicle speed exceeds a predetermined maximum value. The beginning of the retardation is then carried out with the working direction of the gearbox unchanged until the speed has dropped below that maximum, and then the working direction is reversed.
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