A device for winding webs on core tubes includes mutually opposite trunnions (38), which are aligned with each other and rotatably mounted in a machine frame and at their confronting ends are provided with mandrels, which are adapted to be inserted into the core tubes and to be forced against said core tubes. Each of said trunnions is mounted in an axially displaceable bearing sleeve (31). The apparatus also comprises drive means for axially reciprocating at least one of the mutually opposite trunnions. The trunnion is axially slidably and non-rotatably mounted in the bearing sleeve, and the latter is axially slidably and non-rotatably mounted in a bearing bushing (28), which is rotatably mounted in the machine frame.