The present Invention concerns a clamp (20) for mounting upon an elongate member such as a riser (24) to be deployed underwater. The clamp may for example be intended to prevent movement of a buoyancy module along a riser. The clamp comprises a plurality of clamp bodies (22) to be placed at circumferential intervals about the elongate member. A strap (42) is provided which is to be placed around the clamp bodies and tensioned to urge the clamp bodies toward the elongate member, enabling the clamp to resist movement along it. The clamp bodies comprise respective spring elements (28) which are arranged, when the clamp is assembled and mounted, between the clamp bodies and the elongate member. The clamp bodies and the spring elements are shaped to permit them to be used in clamps having a range of different diameters and having a differing number of clamp bodies.