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 (6) and each coupling member (7) comprises engaging means (11-16) for releasable sliding engagement of a coupling member with a bracket member. Each bracket member (6) or each coupling member (7) is provided with resilient means (9) engageable with abutment means (19) of a coupling member (7) or a bracket member (6) to retain the bracket member and the coupling member in mutual engagement. The bracket members (6) are identical standard members each comprising a relatively flat front part protruding from said frame surface (2) and having a substantially smooth external surface and engaging means (11-12) formed by a pair of opposed parallel side edges. Each coupling member (7) is formed as a substantially flat brick-like member provided with an open recess limited by leg portions (13-14) forming engaging means (15-16) engageable with said engaging means on the bracket members.