Hydraulic transmission apparatus (20) including a pump (24) having a variable cylinder capacity and feeding one or more hydraulic motors (26A, 26B), and a control unit (50). In the apparatus, the feed and discharge orifices of the motors are arranged in such a manner that, when the pressures at said orifices are equal, the outlet torque from the motors is zero. To make the apparatus inactive, without physically bypassing the motors, the control unit is suitable for operating the apparatus in a “torque-free” mode by regulating the cylinder capacity of the pump in such a manner that the pressures at said feed and discharge orifices remain substantially equal.