Abstract: The invention relates to machining of surfaces of substantially flat workpieces by means of machining tools which can be driven in rotation, whereby the workpieces and tools are movable relative to one another. In order that a corresponding machining apparatus can be used with relatively low apparatus costs and with optimal machining results for very varied types of surface machining, the workpiece surfaces are machined in the same machining apparatus as required by means of a first tool unit containing a machining roller or (in exchange therefor) by means of a second tool unit containing a group of disc-type machining tools, whereby the machining roller can be positioned approximately in the radial direction and the disc-type machining tools can be positioned approximately in their axial direction against the workpiece surfaces.