The engine began development in the late 1970s for the Republic of China (Taiwan) Air Force AIDC F-CK Indigenous Defence Fighter (IDF), and it first ran in 1979.

The F124/F125 engine has since been proposed for use on other aircraft, such as the T-45 Goshawk and the SEPECAT Jaguar, and currently powers the Aero L-159 Alca and the Alenia Aermacchi M-346.

In 1978, Garrett announced joint research on the TFE1042 afterburner with Swedish company Volvo Flygmotor AB in order to provide an engine for the AIDC F-CK Indigenous Defence Fighter (IDF) being developed for the Republic of China (Taiwan) Air Force (ROCAF).

The TFE731 Model 1042 was touted as a low bypass ratio "military derivative of the proven commercial TFE731 engine" and "provides efficient, reliable, cost effective propulsion for the next generation of light strike and advanced trainer aircraft", with thrust of 4260 lbf (18.9 kN) dry and 6790 lbf (30.2 kN) with afterburner.

[1] AIDC also suggested upgrading TFE1042-7 to 8000 lbf (31 to 36 kN) thrust as twin engine solution, in order to compete with General Electric F404 for applications such as the JAS 39 Gripen.

However, after the IDF order was cut in half due to budget concerns, the TFE1088-12 engine upgrade plan ended as well.

[3] Targeting the 70-130 seat passenger aircraft market, the TFE742 was a 18,000 lbf thrust (80 kN; 8,200 kgf), high-bypass turbofan driven by a gearbox.

[4] In the mid-1990s, AlliedSignal considered developing a turboprop engine for the European Future Large Aircraft military transport (later known as the Airbus A400M), which was to be based on the core of the TFE1042.

[5][6] AlliedSignal, AIDC, and other Asian partners also derived an industrial gas turbine from the TFE1042, initially as the 12,000-horsepower (9-megawatt) AS1042,[7] which evolved into the 13,000 hp (10 MW) ASE120.

[9][10] The possibility of a F124-powered T-45 arose again in 1996 when McDonnell Douglas offered an F124-engined T-45 to the Royal Australian Air Force as a competitor for their trainer requirement.

[19] This proposal of Indian Air Force to up-engine its fleet of SEPECAT Jaguar ground attack aircraft stalled after a decade in August 2019 owing to the high cost involved.