Abstract: A rack for a motor-vehicle roof comprises a pair of bridges (10) each having a cross member (12), a pair of box-shaped feet (14) for bearing on the roof (T) and a connector for hooking and fixing each foot on to the edge (B) of the roof, such as the drainage channel or the upper edge of a door opening. Each cross member (12) is slidably inserted in respective transverse passages formed in the upper parts of the feet (14) and pressure members are associated with each transverse passage, respectively, for clamping the cross member (12) in an adjusted position. The hooking and fixing connector for each bridge (10) is comprised of an inextensible strap (18) which passes through each foot (14), through an opening in an outer wall of the foot and which is provided, outside this outer wall, with a rigid, shaped hook (20), which is replaceable by other similar hooks of different shapes, for hooking on the edge (B) of the roof (T). At least one of the two feet (14) incorporates a device for tensioning the strap (18).