Since the class G was not built in large numbers due to its engine being overly complex, there were still many six-coupled locomotives in use at the beginning of the century. In order to be able to avoid having to pull heavy freight trains in double in the future, a successor to the G was urgently needed and so the class H was developed. The requirements stipulated a 685-tonne train on a gradient of one percent and radii of up to 274 meters with 20 km/h to be moved, which required a power of about 800 hp. 

In contrast to the complicated chassis of the predecessor, all axles were mounted in the main frame and the first, third and fifth were designed to be laterally shiftable according to the Gölsdorf system. Eight examples were built between 1905 and 1909 with a two-cylinder compound engine using saturated steam technology. A distinguishing feature of these locomotives were the two steam domes, which were far apart and were connected with a pipe. The sandboxes were not on the boiler, but on the running boards. During test runs under unfavorable adhesive conditions, 700 tonnes could be towed at 25 km/h up a gradient of one percent, which exceeded the required performance.

From 1909 to 1920, 26 vehicles of a revised design were procured, which were designated as type Hh. They differed from the first series mainly in having a simple engine using superheated steam. The boiler pressure was lowered from 15 to 13 bars and the heating surface was reduced from 168 to 159 m², which nevertheless resulted in the same output.

The Reichsbahn only took over four of the engines from the first construction lot and assigned them the numbers 57 301 to 57 304. They were subsequently converted to superheated steam. 17 of the newer units were taken over, these were given the numbers 57 401 to 57 417 to distinguish them. Due to the advent of more powerful freight locomotives, all units of the classes H and Hh were retired by 1935.