Open roof construction for a vehicle, as well as a sunscreen for use therein

An open roof construction for a vehicle having an opening (2) in its fixed roof (1) comprises a stationary part (3) to be fixed to the roof and an adjustable upper closure element (4) supported by said stationary part (3). Said upper closure element (4) is adjustable between a closed position, in which it closes the roof opening (2), and an open position, in which it opens the roof opening (2) at least partially. A lower closure element, in particular a sun screen (9), is made in the form of a slidable, substantially rigid screen, which is provided with at least one ventilating opening (14) for passing air through the screen. The screen comprises horizontally overlapping parts, at least adjacent to said ventilating opening (14), which prevent direct incidence of light through the screen.