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 a central longitudinal groove, in which groove a central longitudinal strip of the carrier element is disposed, wherein connecting pieces are provided at both ends of the wiper blade, which windscreen wiper device comprises a connecting device for an oscillating wiper arm. The wiper blade at both ends thereof extends beyond the longitudinal strip in order to define at both ends of the wiper blade a space open at one end thereof, wherein the connecting pieces are retained onto the wiper blade so as to tightly close the groove at both ends of the wiper blade against entry of dust and water.