After the express locomotives with the 2-4-0 wheel arrangement could not reach sufficient speeds and the first 4-4-0 locomotives procured could not convince either, the construction of the locomotives later designated as series Ia was commissioned. In most details, they were based on locomotives that had been built for the KFJB from 1879 and bore the numbers 201 to 213. With these, MÁV was able to operate express trains at a speed of 90 km/h for the first time.

The locomotives had an outer frame, outside cylinders and Hall cranks. The first 16 pieces were delivered between 1881 and 1885 and had a boiler pressure of 10.5 bars. A further 185 units were delivered between 1890 and 1905 and had a boiler pressure increased to twelve bars. The Kaschau-Oderberger Bahn procured five identical units from 1895.

In the beginning, the series Ia could be seen in front of the highest-valued express trains. However, the more powerful series Ie was procured while it was still in production, which contested the service of the Ia on the routes originating from Budapest. They were now increasingly used on the connecting routes between the major main routes.

Later, four examples were equipped with superheaters, which increased the towing capacity at 90 km/h on the level from 107 to 161 tonnes. However, a general conversion of the remaining engines did not come about and soon they were only used on branch lines. MÁV retired the last engines in 1952. During the First World War, 79 examples were sent to the CFR in Romania, where they were scrapped by 1945. Six examples ended up in Czechoslovakia, where they were designated as the class 264.5 and were in service until 1937. After the nationalization of the KsOd, five examples of these also came to the CSD and were designated there as the class 254.4.

One of the locomotives which achieved the highest numbers in the Hungarian State Railways was the series IIIq 0-6-0 freight locomotive. It was considered the successor to the IIIe, but in contrast to this had an internal frame. Between 1893 and 1907, MÁV received 247, all of which were manufactured by MÁVAG. The KsOd also purchased 35 identical machines that were delivered between 1899 and 1909 and were also referred to as IIIq. At the MÁV they became the class 325 from 1911.

It was powered by a two-cylinder compound engine. To adapt to different requirements, a blastpipe with a variable cross-section was installed, with which the balance between the counter pressure of the cylinders and the draft could be changed. Due to its excessive complexity, this mechanism was later removed again.

Despite the overhanging cylinders and firebox and the resulting poorer running smoothness, these locomotives were also regularly used to transport passenger trains. After the First World War, 102 had to be given to Romania, 68 to Yugoslavia, nine to Czechoslovakia and three to Poland.

The MÁV ordered a total of 139 six-coupled tender locomotives from MÁVAG for use in front of freight and passenger trains on branch lines. They were based on a GySEV locomotive, but had larger wheels. The cylinders of the compound engine were very far forward, which did not result in smooth running. The locomotives remained in use by the MÁV until the 1950s.

Their sisters, who stayed in Yugoslavia and Romania after the First World War, probably stayed longer. Many came to industrial companies after their service with the state railways. Today only number 7111 still exists, which was in use on a coal railway until 1968 and is now in the Budapest Railway Park.

The XII was a small tank locomotive for service on secondary lines, which was produced in large numbers by almost every factory in Austria-Hungary. However, it was only used outside the Austrian part of the Reich, since the MÁV had received 549 locomotives and the KsOd 13. It only got its striking appearance later through the installation of a long smokebox that protruded over the buffer beam. After the First World War, the majority was located in Hungary, Czechoslovakia and Yugoslavia. The state railways usually retired the locomotives in the fifties, but in industry they could last into the seventies.