The TVa or later class 376 was designed for branch lines where the maximum allowed axle loading of eleven tonnes of the TV or class 375 was still too high. It had a similar layout as a 2-6-2T tank locomotive, but was made smaller and lighter to get an axle loading of only nine tonnes. Like the TV, the original variant of the TVa was also a saturated two-cylinder compound. 

The MÁV received a total of 319 locomotives of this class from MÁVAG. The first 208 built between 1910 and 1913 were of the original saturated compound variant, while 111 more built between 1914 and 1924 were superheated simples. 28 of these which had been built in the war had received a Brotan boiler. Eleven more of the original variant were built between 1912 and 1914 for the Košice–Bohumín Railway (KsOd).

The top speed was originally set at 45 km/h and was increased to 50 km/h in 1930. On the level they were able to haul 480 tonnes at top speed, what decreased to 250 tonnes at 20 km/h on 1.5 percent. Over time, locomotives of the original variant were superheated and simpled. Additionally, they got several smaller improvements to increase their efficiency.

After World War I, they were each around 100 locomotives in Hungary, Romania and Yugoslavia. 20 were in Czechoslovakia, which also included the KsOd locomotives, and one in Poland. The ČSD received the KsOd locomotives when this railway was nationalized in 1924. The MÁV retired this class in 1966, the locomotives of the CFR were the last ones which were retired in 1975.