Abstract: According to the method for controlling an automatic cleaning device while a window surface is being cleaned, the cleaning head is first advanced in force-controlled manner approximately centrally or near the edge towards the window surface. This initial position follows from the basic data of the associated building on the basis of the constructional drawing. The cleaning head is then moved in the X- or Z-direction over the window surface up to the window frame in a first edge-search mode and then along the window frame into the associated window corner in which the cleaning process proper starts. The frame of the cleaning head is elastically displaceable relative to the rigid structure so that the control means can sense whether the cleaning head is in contact with a window edge. Alternatively, in the case of frameless windows, there may be provided a sensor whose signal is received by the control means.