It is a roof for a vehicle comprising several roof elements (1, 2, 3) that can be displaced between a first position above the passenger compartment and a second position in which they are stowed inside the boot (160), the roof elements being, when they cover the passenger compartment, connected to each other and to respectively front and rear parts (40, 42) of the body structure (120) of the vehicle via means for securing controlled by rigid rods (5, 60, 10, 11, 12) driven by the controlling means (4). These rods are constantly connected to each other in pairs from one of the roof elements to another, as much in the first position as in the second position of these elements, by flexible means (8, 9) transmitting the movement generated by the controlling means (4) between the rods and allowing to secure said roof elements to the body structure (120) of the vehicle, as much in their first as in their second positions.