The rewinder machine comprises: a first winding roller (3); a second winding roller (5), defining with said first winding roller (3) a winding cradle; a feeder (33) for sequentially introducing winding cores to said winding cradle; an optional glue applicator (21) for applying glue to said cores. The feeder (33) may include an element (39) for applying glue to the winding cores while they are being fed to said winding cradle. In a special embodiment, the feeder is mechanically linked to a system for unloading the roll from the winding cradle.