An apparatus is intended to produce a multi-layer extrudate comprising an intermediate material interposed between at least two layers of outer material. The apparatus comprises an arrangement of ducts which includes a first duct and a second duct through which respective lateral flows of outer material can flow. The arrangement of ducts also includes a further duct through which a central flow comprising at least the intermediate material can flow. The apparatus further comprises at least one obstructing element for interacting at least with the central flow while the central flow is advancing in an advancement direction. The at least one obstructing element is movable with a movement having a component directed transversally to the advancement direction, so as to obstruct the central flow in the advancement direction at preset intervals.