Supporting means for a window screening device comprises a first pair of bracket members (6) for mounting on each of a pair of opposed parallel frame surfaces (2) of said frame structure and a second pair of coupling members (7) engageable by said screening device. Each bracket member comprises a relatively flat front part protruding from the frame surface and having a substantially smooth external surface, whereas the engaging means (11-12; 111-112; 33-34) is provided by each coupling member (7; 107; 207; 307; 36) and comprises first engaging means in the form of at least one contact surface on the coupling member engaging a circumferential surface part of a bracket member to provide temporary engagement therewith and non-resilient second engaging means providing stable engagement of the coupling member with respect to the frame structure.