A hydrostatic traction drive device of a mobile machine has a first hydraulic traction motor associated with a first vehicle side and a second hydraulic traction motor associated with a second vehicle side. The hydraulic traction motors are operated in an open circuit and are jointly supplied with hydraulic fluid by a single hydraulic pump. The first hydraulic traction motor is controlled by a first control valve and the second hydraulic traction motor is controlled by a second control valve. The first hydraulic traction motor and the second hydraulic traction motor are each variable displacement motors with an electrically variable displacement volume, and the first control valve and the second control valve are electrically actuatable control valves. The device is provided with an electronic control device which controls the displacement volumes of two traction motors and controls the control valves. The electronic control device is configured that the input side pressure forces of the two traction motors in turning driving are in the same pressure level through changing the displacement volume of one of the two traction motors and controlling the associated control valve.