A transmission for speed changing and steering of a vehicle comprises a first HST and a first differential for speed changing and a second HST and a second differential for steering. The first HST is a combination of a hydraulic pump and motor. The pump is driven by an engine and the motor is drivingly changeable by operation of a speed change pedal. Output power from the motor is transmitted into a pair of first differential output shafts as axles through the first differential. The second HST is a combination of a hydraulic pump and motor. The second pump is driven by output power from the first HST and the second motor is drivingly changeable by operation of a steering wheel. A pair of second differential output shafts are rotated in opposite directions by output power of the motor, so that when turning, the first differential output shaft on the opposite side of the turning direction is accelerated.