In order to provide a structure for removable attachment to a substantially vertical surface for example of glass, glazed tiles or metal, the structure has a mounting means comprising: suction means (1) for sealingly contacting a surface, pulling means (2) being attached to the suction means (1) for drawing a part of the suction means (1) away from the surface, so that a partial vacuum is created between the suction means (1) and the surface. There is a substantially helical or wedge shaped surface on the pulling means (2) engaged with a corresponding substantially helical or wedge shaped surface of a rotatable member (13), whereby rotation of the rotatable member (13) draws the pulling means (2) and respective part of the suction means (1) away from the surface. An intermediate member (5) is provided for engaging a sealing part of the suction means (1), the intermediate member (5) supporting the rotatable member (13). The structure comprises a structural member (10) mounted in or on the intermediate member (5), so that the structural member (10) is not gripped by the intermediate member (5) or rotatable member (13). At least part of the rotatable member extends beyond a part of the intermediate member which is adjacent to the rotatable member. There is a friction reducing member (11) between the rotatable member and the intermediate member. A clip means, possibly also acting as a friction reducing member (11), can be provided for holding the structural member 18 temporarily in position on the intermediate member 5 during assembly.