The wiper device includes a carrier element and a wiper blade with at least one longitudinal groove, in which groove the carrier element is disposed. The wiper device also includes a connecting device for pivotally connecting the wiper blade with an oscillating arm. The connecting device has spaced-apart sidewalls, each with a protrusion that extends sidewardly and outwardly. The connecting device and oscillating arm are interconnected by the protrusions pivotally and snappingly engaging into correspondingly shaped recesses of the oscillating arm. The oscillating arm has a guiding tongue engaging into a guiding groove of the connecting device. The connecting device has an asymmetric form with respect to its middle transverse plane, seen in vertical direction, in order to ensure that the wiper blade can only be mounted on the oscillating arm in a predetermined orientation of the wiper blade relative to the oscillating arm.