A hydrostatic transmission device of a mobile machine having —at least one first motor and at least one second motor, —at least one first dual motor and at least one second dual motor each having first and second elementary motor, —the second elementary motor of the first dual motor is linked with the first motor by a serial duct, —the second elementary motor of the second dual motor is linked with the second motor by a serial duct, —each serial duct has a valve having an opening for passage of the fluid into the serial duct, said valve having a first position in which said opening has a maximum cross-section, and a second position in which said opening has a reduced cross-section, the movement of said valve between these two positions activated a control instruction generated when the machine is travelling on a slope.