An axle driving apparatus comprising a combination of a speed-change HST for coupling a variable-capacity pump and a motor with a fluid on the one hand and a steering HST for coupling a variable-capacity pump and a motor with a fluid on the other hand, configured in such a manner that the two HSTs are accommodated in a common housing. The motor output of the speed-change HST is transmitted to a differential arrangement for differentially coupling a pair of axles, and the motor output of the steering HST is transmitted to a differential arrangement for differentially coupling a pair of steering output shafts. One of the steering output shafts and one of the axles are power-coupled to one transmission train, while the other steering output shaft and the other axle are power-coupled to the other transmission train which applies a turning effort to the other axle in the direction opposite to the turning effort applied to the first axle by the first transmission train. The capacity adjusting means of the pump of the steering HST is operatively interlocked with a steering operation means such as a steering wheel, so that the capacity adjusting means is rotated in one direction in forward drive and in the other direction in rearward drive when the steering wheel is manipulated in a predetermined direction.