The history of 1 Fighter Squadron (1 SLt) - Slovak Air Force dates back to October 1992 when Slovak pilots underwent a conversion course for the MiG 29 Fulcrum held at Zatec AFB, in the former Czechoslovak Federal Republic, which subsequently became the base of 1 SLt at Sliač AFB.

The Fulcrums where flown to Sliač AFB in December 1992. Only a few days later on January 1st, Czechoslovakia peacefully split into the Czech Republic and Slovakia, this resulting in the diversion of the Czechoslovak Armed Forces. Over the next two years their designation changed from 1 St Fighter Squadron (1 Stíhacia Letka) to be renamed in early 1995 as 311 Stíhacia Letka (1st Squadron of the 31st Fighter Wing) and finally in October 2001 to the 1 Stíhacia Letca of the Stíhacie Letecké Krídlo (Fighter Wing).