A bale-wrapping machine (1) is disclosed for wrapping a bale of material (6). The machine comprises a means (5) for engaging the bale and rotating it about a substantially horizontal axis. A main rotary wrapping arm (7) is disposed for supplying a first strip of wrapping material (10) to the bale (6) as it is turned and an auxiliary rotary wrapping arm (12) is disposed for supplying a second strip of wrapping material (10). The auxiliary arm (12) can be pivoted relative to the main arm (7) between a rest' position (as shown) adjacent to the main arm and a wrapping position. In the wrapping position the auxiliary arm (12) is arranged substantially opposite to the main arm (7).