An axle driving apparatus for being mounted on the body frame of a vehicle and for independently rotating drive wheel members. The axle driving apparatus includes a first axle driving unit (18L) having a housing (40) and a single axle (20L), the single axle (20L) defining a proximal end portion rotatably mounted in the housing (40) and a distal end portion extending outwardly from a first side of the housing (40). An enlarged region is defined by the housing (40), with the enlarged region extending substantially perpendicular to the longitudinal axis of the single axle (20L). A hydraulic stepless speed change assembly (22) is disposed within the enlarged region. The speed change assembly (22) includes a hydraulic pump (52) having an input shaft (21) projecting from the enlarged region and includes a hydraulic motor (55) including an output shaft (74) drivingly connected to the single axle (20L). The first axle driving unit (18L) is used in conjunction with a second axle driving unit (18R) which is adjacently disposed to the first axle driving unit (18L) on the body frame of the vehicle and which is of substantially similar construction. However, the second axle driving unit (18R) features a single axle (20R) which extends outwardly from a second, opposite side of the housing (40) such that the axles (20L, 20R) are oppositely disposed.