A method for managing the continuous feeding of an elongate element wound on reels to a station for building a tire, wherein the elongate element is continuously supplied from an unwinding device of successive reels. When the terminal end of the elongate element wound on a first reel leaves said first reel, the method provides for: the first reel to be moved away from the unwinding device on a first movable carriage; a second reel, successive to the first reel, and mounted on a second movable carriage, to be positioned in place of the first reel; and the terminal end of the elongate element previously wound on the first reel, to be joined to the starting end of the elongate element wound on the second reel.