A screen device intended for a window or a door in a building or vehicle. The device includes a first elongated frame part having two ends; a further frame part and a third one, respectively, being arranged at each end of the first frame part at right angles to the first frame part and connected to a first one of its two ends. Two crossbars are arranged in parallel to the fixedly arranged first frame part and movable independently of each other along the two further frame parts. A pleated screen element is arranged between the first crossbar and the second crossbar, and the crossbars are guided by guide cords. At least one of the crossbars is formed by two profiles that are arranged in parallel to each other and leave a space between them in which a strip provided with holes for respective ones of the guide cords is received.