A method of examining a wafer of crystalline semiconductor material by means of X-rays, in which method a surface of the wafer is scanned by means of an X-ray beam and secondary radiation generated by said X-ray beam is detected. Prior to the examination the surface of the wafer which is to be scanned by the X-ray beam during the examination is glued to a substrate, after which crystalline semiconductor material is removed at the side which is then exposed, removal taking place as far as the top layer which adjoins the surface. The top layer can thus be examined without the examination being affected by crystal defects or impurities present in layers of the wafer which are situated underneath the top layer.