A security device for mounting over the neck of a bottle having an exterior lip has outer cap structure including an annular housing portion (16) for location about the neck of a bottle and an end cap portion (18) at one end of the annular housing portion. A claw member (14) is slidably mounted to the outer cap structure for movement in a direction parallel to a longitudinal axis of the annular housing portion between operative and inoperative positions. A latch mechanism (60) releasably secures the claw member in the operative position. The claw member has a plurality of resiliently deformable elongate claws (52a, 52b) for engagement with the neck of a bottle to which the device is mounted when the claw member is in the operative position. The claw member comprises at least two sets of claws (52a, 52b) of different lengths. The latch mechanism (60) may be a magnetically-releasable latch enabling the device to be removed using a magnetic key. The device may incorporate a RF or RFID tag.