A method for feeding elastic threads in a process for the production of layered composite articles includes: feeding at least one elastic thread along a path extending from a reel of an elastic thread up to a joining zone with at least one web material. Feeding the elastic thread along the above path includes: giving the elastic thread a first percentage elongation along a first section of the path extending between the reel and a control zone; giving the elastic thread a second percentage elongation along a second section of the path extending between the control zone and the joining zone. The second percentage elongation is greater than the first percentage elongation and a length of the first section is greater than a length of the second section.