When the Crampton locomotives used for express trains on the Grand Duchy of Baden State Railways were no longer state of the art, a new express locomotive was developed from the class III passenger locomotives.

Special features of the II a were the Belpaire firebox and an outer plate frame. The power was transmitted via Hall cranks to the drivers located within the frame. Because the cylinders were located in front of the pivot of the lead bogie, the running smoothness was not entirely convincing. Especially under full load, the overhanging masses of the cylinders generated unwanted vibrations.

Despite this, the locomotive performed well and was used on the international trains that traversed the Baden region. The locomotives were able to pull a 220-tonne train with 16 cars on the flat at up to 84 km/h and thus still reached 60 km/h on a gradient of 0.5 percent. At 1.25 percent, 150 tonnes could still be pulled at 50 km/h.

Another delivery of ten locomotives in 1891 saw the need to lengthen the boiler tubes and increase the diameter of the cylinders to 457 mm. To improve the running characteristics, the wheel base of the bogie was also increased from 1,400 to 2,000 mm.

After the founding of the Reichsbahn, the II a met the same fate as other older Länderbahn locomotives. Of the 24 units built, ten were still included in the renumbering plan as class 36⁷³. Eventually all were retired by 1925.