The present invention relates to a bale-wrappingmachine (1) for wrapping a bale (6) of materialwith a wrapping material. The machine comprises means(5) for engaging a bale for wrapping and for rotating thebale about a substantially horizontal axis. The machinefurther comprises a main rotary wrapping arm (7) forsupplying a first strip of wrapping material to the bale asthe bale is turned about the horizontal axis and anauxiliary rotary wrapping arm (12) for supplying a secondstrip of wrapping material to the bale as the bale isturned about the horizontal axis. The auxiliary arm (12)is pivotable relative to the main arm (7), such that theauxiliary arm is moveable between a 'rest' position, inwhich it is arranged adjacent to the main arm, and awrapping position, in which the auxiliary arm is arrangedsubstantially opposite the main arm.