The type S 2 of the Prussian State Railways designated several express locomotives built between 1890 and 1902. The first two locomotives which later got the designation S 2 were built in 1890 for the Hanover directorate. They had been designed by August von Borries and were two-cylinder compounds. Being the first 4-4-0 locomotives in Prussia, they also had a new type of bogie, here called the Hanover-bogie. Because the starting problem of two-cylinder compounds hadn't been fully solved at this time, no additional locomotives were built and the existing two survived until 1912.

In 1891, in parallel with the trials with the Erfurt type of the P 4.1, an express variant was designed that was later called the Erfurt type of the S 2. Like the S 2 Hanover type, it had drivers of 1,960 mm in contrast to the 1,730 mm of the P 4.1. Two were built as two-cylinder compounds and two as two-cylinder simples.

Also in this case, the simple variant won and 148 more were built until 1893. The production only ended due to the introduction of the more powerful S 3. However, 26 of the simple S 2 were later rebuilt into compounds. One additional locomotive was built with a Lentz stayless boiler that wasn't judged as a success. Only seven of the compound variant made it into the Reichsbahn numbering plan of 1923 as 13 001 to 13 007. Only 13 001 actually got its new number, but was retired in 1926.

15 more locomotives which were later also called S 2 had the wheel arrangement 2-4-2 instead and had been built for the Main-Neckar-Eisenbahn-Gesellschaft between 1892 and 1902. They were based on the Belgian type 12 and the first eight had been built by Cockerill in Belgium, while the other seven came from the MBG Karlsruhe. When this railway had been split among the Baden and the Prussian railways, these locomotives came to Prussia and were nicknamed “Krokodil” (crocodile) due to the name of their original builder.