A windscreen wiper device comprising an elastic, elongated carrier element, as well as an elongated wiper blade of a flexible material, which can be placed in abutment with a windscreen to be wiped, which wiper blade includes at least one longitudinal groove, in which groove a longitudinal strip of the carrier element is disposed, which windscreen wiper device comprises a connecting device for an oscillating arm, wherein the oscillating arm can be pivotally connected to the connecting device about a pivot axis near one end, with the interposition of a joint part, with the special feature that the connecting device has a substantially H-shaped cross-section, wherein lower legs of the H-shaped cross-section are connected to the flexible material of the wiper blade on opposite sides thereof, and wherein upper legs of the H-shaped cross-section are adapted to receive the joint part.