The Category-A listed units are the only surviving examples of this building type left in Scotland.
Now Army Defence Services has submitted a planning application to Fife Council to carry out internal and external repairs to Hangars 55 and 57.
A report revealed the roof coverings are “clearly at the end of their life” with many of the panels severely corroded, and the priority is to make the building watertight “to avoid any further deterioration of the historic fabric.”
Leuchars Station is currently a British Army barracks, but it was originally built as an RAF base.
Before its closure, it had a tradition of over a century of use for aviation and was one of the longest continuously operating military airfields in the world.
Flying began in the Leuchars area in the earliest days of manned flight.
In 1909 the very first purpose-built aerodrome in the UK had been built at Larkhill in Wiltshire, and two years later the Royal Engineers balloon squadron began launching flights from Leuchars.
In 1916 work began to create a new aerodrome at Reres Farm, south east of Leuchars village. The ground was levelled, and runways set out, as a priority to get the airfield operational.
Construction of the general service sheds started towards the end of 1917.
The RAF occupied the site until the last air defence squadrons left the station in 2014.
The following year, it was taken over by the British Army.
Hangars 55 and 57 are the last two remaining pairs of the original three constructed on the site during World War One.
The central hangar pair and accompanying workshop were demolished in 1973.
A design statement said RAF Leuchars has “an outstanding collection of airfield structures covering aviation and military history from the First World War right through until the Cold War period and beyond.”It added: “Within Scotland it is one of the best-preserved airfields and in UK terms it is considered to be in the top ten most important sites.”
Councillors will consider the application in due course.