A sunshade assembly includes a sunscreen having opposed longitudinal edges which are provided with guide strips which are substantially rigid in transverse direction. Opposed longitudinal guiderails each include a guide channel section defining a guide channel in which the respective guide strip is accommodated when the sunscreen is moved between open and closed positions. The guide channel of each guide rail is bound on the side facing the opposite guiderail by a guide flange supporting the lower side of the sunscreen. A part of the guide channel supports the guide strip on its side remote from the sunscreen. A biasing member acts between at least one of the guide strips and the corresponding guide channel section to bias the guide strip at least on its edge adjacent the sunscreen in a direction away from the guide flange.