An axle driving apparatus in which an oil sump provided in a housing is vertically partitioned into first and second chambers by partition means constructed in the housing. The first chamber is constructed to have an air layer open to the atmosphere, the second chamber is constructed to be always filled with oil. The first chamber and second chamber can flow oil therebetween through an oil introduction passage of the partition means. When oil volume expands by the temperature during the operation of a hydrostatic transmission, while reducing the volume of the air layer in the first chamber, the oil in the second chamber adjustably flows into the first chamber.