A method for managing elongate elements in a plant for building tyres, comprises: • - providing a device (100) for storing and supplying at least one elongate element (3) comprising a first rotation shaft (14) and a second rotation shaft (15) which are coaxial and which can be controlled selectively between a first operating configuration, in which the first rotation shaft and the second rotation shaft are fixedly joined to each other, and a second operating configuration, in which said shafts can freely rotate independently of each other, • - maintaining the first rotation shaft (14) and the second rotation shaft (15) in the first operating configuration when the device (100) is in storage and transport operation and • - moving the first rotation shaft (14) and the second rotation shaft (15) into the second operating configuration when the device (100) is in the course of winding or unwinding said at least one elongate element on or from the first or second rotation shaft.