A hydraulic driving apparatus for a wheeled vehicle including a prime mover and a pair of wheels comprises a stepless transmission mechanism for traveling which transmits driving force from the prime mover to the drive wheels so as rotate the drive wheels in a common forward or rearward direction, and a steering transmission mechanism including a hydrostatic stepless transmission including a variable hydraulic pump and a hydraulic motor fluidly connected to each other, wherein a rotational force of the hydraulic motor is divided into opposite directive rotations transmitted to the respective drive wheels. A switching valve is disposed between the variable hydraulic pump and the hydraulic motor in the steering transmission mechanism. The switching valve reverses the rotational direction of the motor relative to the discharge direction from the pump according to a change in the traveling direction of the vehicle between forward and rearward, and divides a pair of oil passages between the pump and the motor into independent circuits which include the pump and the motor, respectively.